Let G be the direct sum of the noncyclic groupof order four and a cyclic groupwhoseorderisthe power pn of some prime p. We show that ℤ2G-lattices have a decidable theory when the cyclotomic polynomia equation image is irreducible modulo 2ℤ for every j ≤ n. More generally we discuss the decision problem for ℤ2G-lattices when G is a finite group whose Sylow 2-subgroups are isomorphic to the noncyclic group of order four.

Let n be a positive integer and FAℓ be the free abelian lattice-ordered group on n generators. We prove that FAℓ and FAℓ do not satisfy the same first-order sentences in the language if m≠n. We also show that is decidable iff n{1,2}. Finally, we apply a similar analysis and get analogous results for the free finitely generated vector lattices.

In [GK], Gurevich and Kokorin proved that any two non-trivial ordered abelian groups (o-groups, for short) satisfy the same existential sentences. Let nowG, H be non-trivialo-groups with a commono-subgroupG 0. We determine whetherG andH are existentially equivalent overG 0. As a corollary, we obtain algebraic criteria for deciding, whether ano-subgroupG is existentially closed in ano-groupH. Corresponding results are proved foro-groups in which congruences are regarded as atomic relations.

We extend the analysis of the decision problem for modules over a group ring ℤ[G] to the case when G is a cyclic group of squarefree order. We show that separated ℤ[G]-modules have a decidable theory, and we discuss the model theoretic role of these modules within the class of all ℤ[G]-modules. The paper includes a short analysis of the decision problem for the theories of modules over ℤ[ζm], where m is a positive integer and ζm is a primitive mth (...) root of 1. (shrink)

ABSTRACT This paper reconstructs William of Ockham's (c. 1287–1347) account of the ontology of social groups. Across his writings, Ockham mentions kingdoms, religious orders, crowds, people, armies, and corporations. Using the political community as a case-study against the background of Ockham’s metaphysics of parts and wholes, it is argued that at least some social groups are identical to a plurality of many human beings who have decided to order themselves with respect to another in some particular way. In (...) this regard, a social group is a structured aggregate that is nothing over and above its existing and ordered parts, and, at least in the case of the political community, is like an artefact inasmuch as it is partly dependent on the volitional acts of its members to exist at all. (shrink)

We consider the decision problem for modules over a group ring ℤ[G], where G is a cyclic group of prime order. We show that it reduces to the same problem for a class of certain abelian structures, and we obtain some partial decidability results for this class.

For arbitrary finite group $G$ and countable Dedekind domain $R$ such that the residue field $R/P$ is finite for every maximal $R$ -ideal $P$ , we show that the localizations at every maximal ideal of two $RG$ -lattices are isomorphic if and only if the two lattices satisfy the same first order sentences. Then we investigate generalizations of the above results to arbitrary $R$ -torsion-free $RG$ -modules and we apply the previous results to show the decidability of the theory (...) of ${\vec Z}C(2)^2$ -lattices. Eventually, we show that ${\vec Z} [i] C(2)^2$ -lattices have undecidable theory. (shrink)

An Ax-Kochen-Ershov principle for intermediate structures between valued groups and valued fields. We will consider structures that we call valued B-groups and which are of the form $\langle G, B, *, v\rangle$ where - G is an abelian group, - B is an ordered group, - v is a valuation defined on G taking its values in B, - * is an action of B on G satisfying: ∀ x ∈ G ∀ b ∈ B v(x * (...) b) = v(x) · b. The analysis of Kaplanski for valued fields can be adapted to our context and allows us to formulate an Ax-Kochen-Ershov principle for valued B-groups: we axiomatise those which are in some sense existentially closed and also obtain many of their model-theoretical properties. Let us mention some applications: 1. Assume that v(x) = v(nx) for every integer n ≠ 0 and x ∈ G, B is solvable and acts on G in such a way that, for the induced action, $\mathbb{Z}[B] \setminus \{0\}$ embeds in the automorphism group of G. Then $\langle G, B, *, v\rangle$ is decidable if and only if B is decidable as an ordered group. 2. Given a field k and an ordered group B, we consider the generalised power series field k((B)) endowed with its canonical valuation. We consider also the following structure: $\mathbf{M} = \langle k((B))_+, S, v, \times \upharpoonright_{k((B))\times S}\rangle,$ where k((B)) + is the additive group of k((B)), S is a unary predicate interpreting ${T^b| b \in B}$ , and $\times \upharpoonright_{k((B))\times S}$ is the multiplication restricted to k((B))× S, structure which is a reduct of the valued field k((B)) with its canonical cross section. Then our result implies that if B is solvable and decidable as an ordered group, then M is decidable. 3. A valued B-group has a residual group and our Ax-Kochen-Ershov principle remains valid in the context of expansions of residual group and value group. In particular, by adding a residual order we obtain new examples of solvable ordered groups having a decidable theory. (shrink)

We present a simplification and a modification of a method introduced by Herzig to prove the decidability of Quine’s ordered fragment of first-order logic. The method consists in an interpretation of quantifiers as modal operators. We show that our modification yields the decidability of two new ordered fragments of first-order logic, called the grooved fragment and the loosely grooved fragment, whose expressive power lies between Quine’s ordered fragment and the fluted fragment.

We consider R-torsionfree modules over group rings RG, where R is a Dedekind domain and G is a finite group. In the first part of the paper [4] we compared the theory T of all R-torsionfree RG-modules and the theory T0 of RG-lattices , and we realized that they are almost always different. Now we compare their behaviour with respect to decidability, when RG-lattices are of finite, or wild representation type.

Humans routinely make many decisions collectively, whether they choose a restaurant with friends, elect political leaders or decide actions to tackle international problems, such as climate change, that affect the future of the whole planet. We might be less aware of it, but group decisions are just as important to social animals as they are for us. Animal groups have to collectively decide about communal movements, activities, nesting sites and enterprises, such as cooperative breeding or hunting, that crucially affect (...) their survival and reproduction. While human group decisions have been studied for millennia, the study of animal group decisions is relatively young, but is now expanding rapidly. It emerges that group decisions in animals pose many similar questions to those in humans. The purpose of the present issue is to integrate and combine approaches in the social and natural sciences in an area in which theoretical challenges and research questions are often similar, and to introduce each discipline to the other’s key ideas, findings and successful methods. In order to make such an introduction as effective as possible, here, we briefly review conceptual similarities and differences between the sciences, and provide a guide to the present issue. (shrink)

Objectives—The development of predictive genetic tests provides a new area where consumers can gain knowledge of their health status and commercial opportunities. “Over-the-counter” or mail order genetic tests are most likely to provide information on carrier status or the risk of developing a multifactorial disease. The paper considers the social and ethical implications of individuals purchasing genetic tests and whether genetic information is different from other types of health information which individuals can obtain for themselves.Design—The discussion is illustrated by findings (...) from a questionnaire survey of university students as potential consumers. Topics covered included what health tests they had already used, expectations of genetic tests, willingness to pay, who should have access to the results and whether there need to be restrictions on such tests.Sample—Six hundred and fifteen first-year students in the universities of Leuven, Cardiff, Central Lancashire, Vienna and Nijmegen studying either medicine or a non-science subject.Results—Students were enthusiastic about genetic tests and had high expectations of their accuracy and usefulness but most thought they should be available through the health service and a minority thought that some tests, for example for sex selection, should not be available at all. There were few differences in responses by sex or subject of study but some by country. The paper also considers ethical and social issues outside the scope of a questionnaire survey of this type.Conclusion—To address some of these issues the sale of genetic tests to individuals can be made subject to ethical guidelines or codes of practice, for example to protect vulnerable groups, but there are fundamental social and ethical questions which such guidelines cannot address. (shrink)

Beliefs are commonly attributed to groups or collective entities. But what is the nature of group belief? Summativism and nonsummativism are two main rival views regarding the nature of group belief. On the one hand, summativism holds that, necessarily, a group g has a belief B only if at least one individual i is both a member of g and has B. On the other hand, non-summativism holds that it is possible for a group g to have a belief (...) B even if no member of g has B. My aim in this paper is to consider whether divergence arguments for non-summativism and against summativism about group belief are sound. Such divergence arguments aim to show that there can be a divergence between belief at the group level and the corresponding belief at the individual level. I will argue that these divergence arguments do not decisively defeat a minimal version of summativism. In order to accomplish this goal, I have the following plan: In section 2, I will analyze the structure of two important counterexamples against the summativist view, which are based on divergence arguments. Such counterexamples are based on the idea that a group decides to adopt a particular group belief, even if none of its members holds the belief in question. However, in section 3, I will show that these counterexamples fail, because they can be explained without the need to posit group beliefs. More specifically, I argue that in these apparent counterexamples, we have only a ‘group acceptance’ phenomenon and not a ‘group belief’ phenomenon. For this conclusion, I advance two arguments: in subsection 3.1, I formulate an argument from doxastic involuntarism, and in subsection 3.2, I develop an argument from truth connection. Thus, summativism is not defeated by divergence arguments. Lastly, in section 4, I will conclude with some advantages of summativism. (shrink)

We prove that a finitely generated group is context-free whenever its Cayley-graph has a decidable monadic second-order theory. Hence, by the seminal work of Muller and Schupp, our result gives a logical characterization of context-free groups and also proves a conjecture of Schupp. To derive this result, we investigate general graphs and show that a graph of bounded degree with a high degree of symmetry is context-free whenever its monadic second-order theory is decidable. Further, it is shown that the (...) word problem of a finitely generated group is decidable if and only if the first-order theory of its Cayley-graph is decidable. (shrink)

Let G be a finite group. We prove that the theory af abelian-by-G groups is decidable if and only if the theory of modules over the group ring ℤ[G] is decidable. Then we study some model theoretic questions about abelian-by-G groups, in particular we show that their class is elementary when the order of G is squarefree.

Qualitative Reasoning (QR) is an area of research within Artificial Intelligence that automates reasoning and problem solving about the physical world. QR research aims to deal with representation and reasoning about continuous aspects of entities without the kind of precise quantitative information needed by conventional numerical analysis techniques. Order-of-magnitude Reasoning (OMR) is an approach in QR concerned with the analysis of physical systems in terms of relative magnitudes. In this paper we consider the logic OMR_N for order-of-magnitude reasoning with the (...) bidirectional negligibility relation. It is a multi-modal logic given by a Hilbert-style axiomatization that reflects properties and interactions of two basic accessibility relations (strict linear order and bidirectional negligibility). Although the logic was studied in many papers, nothing was known about its decidability. In the paper we prove decidability of OMR N by showing that the logic has the strong finite model property. (shrink)

-/- Continuous first-order logic has found interest among model theorists who wish to extend the classical analysis of “algebraic” structures (such as fields, group, and graphs) to various natural classes of complete metric structures (such as probability algebras, Hilbert spaces, and Banach spaces). With research in continuous first-order logic preoccupied with studying the model theory of this framework, we find a natural question calls for attention. Is there an interesting set of axioms yielding a completeness result? -/- The primary purpose (...) of this article is to show that a certain, interesting set of axioms does indeed yield a completeness result for continuous first-order logic. In particular, we show that in continuous first-order logic a set of formulae is (completely) satisfiable if (and only if) it is consistent. From this result it follows that continuous first-order logic also satisfies an approximated form of strong completeness, whereby Σ⊧φ (if and) only if Σ⊢φ ∸2−n for all n < ω. This approximated form of strong completeness asserts that if Σ⊧φ, then proofs from Σ, being finite, can provide arbitrarily better approximations of the truth of φ. -/- Additionally, we consider a different kind of question traditionally arising in model theory—that of decidability. When is the set of all consequences of a theory (in a countable, recursive language) recursive? Say that a complete theory T is decidable if for every sentence φ, the value φ T is a recursive real, and moreover, uniformly computable from φ. If T is incomplete, we say it is decidable if for every sentence φ the real number φ T o is uniformly recursive from φ, where φ T o is the maximal value of φ consistent with T. As in classical first-order logic, it follows from the completeness theorem of continuous first-order logic that if a complete theory admits a recursive (or even recursively enumerable) axiomatization then it is decidable. (shrink)

We provide algebraic conditions ensuring the decidability of the theory of modules over effectively given Prüfer (in particular Bézout) domains whose localizations at maximal ideals have dense value groups. For Bézout domains, these conditions are also necessary.

The main result of the paper states that there is a finitely presented group _G_ with decidable word problem where detection of finite subsets of _G_ which generate amenable subgroups is not decidable.

Objectives—The development of predictive genetic tests provides a new area where consumers can gain knowledge of their health status and commercial opportunities. “Over-the-counter” or mail order genetic tests are most likely to provide information on carrier status or the risk of developing a multifactorial disease. The paper considers the social and ethical implications of individuals purchasing genetic tests and whether genetic information is different from other types of health information which individuals can obtain for themselves.Design—The discussion is illustrated by findings (...) from a questionnaire survey of university students as potential consumers. Topics covered included what health tests they had already used, expectations of genetic tests, willingness to pay, who should have access to the results and whether there need to be restrictions on such tests.Sample—Six hundred and fifteen first-year students in the universities of Leuven, Cardiff, Central Lancashire, Vienna and Nijmegen studying either medicine or a non-science subject.Results—Students were enthusiastic about genetic tests and had high expectations of their accuracy and usefulness but most thought they should be available through the health service and a minority thought that some tests, for example for sex selection, should not be available at all. There were few differences in responses by sex or subject of study but some by country. The paper also considers ethical and social issues outside the scope of a questionnaire survey of this type.Conclusion—To address some of these issues the sale of genetic tests to individuals can be made subject to ethical guidelines or codes of practice, for example to protect vulnerable groups, but there are fundamental social and ethical questions which such guidelines cannot address. (shrink)

There is currently much interest in bringing together the tradition of categorial grammar, and especially the Lambek calculus, with the recent paradigm of linear logic to which it has strong ties. One active research area is designing non-commutative versions of linear logic (Abrusci, 1995; Retoré, 1993) which can be sensitive to word order while retaining the hypothetical reasoning capabilities of standard (commutative) linear logic (Dalrymple et al., 1995). Some connections between the Lambek calculus and computations in groups have long (...) been known (van Benthem, 1986) but no serious attempt has been made to base a theory of linguistic processing solely on group structure. This paper presents such a model, and demonstrates the connection between linguistic processing and the classical algebraic notions of non-commutative free group, conjugacy, and group presentations. A grammar in this model, or G-grammar is a collection of lexical expressions which are products of logical forms, phonological forms, and inverses of those. Phrasal descriptions are obtained by forming products of lexical expressions and by cancelling contiguous elements which are inverses of each other. A G-grammar provides a symmetrical specification of the relation between a logical form and a phonological string that is neutral between parsing and generation modes. We show how the G-grammar can be oriented for each of the modes by reformulating the lexical expressions as rewriting rules adapted to parsing or generation, which then have strong decidability properties (inherent reversibility). We give examples showing the value of conjugacy for handling long-distance movement and quantifier scoping both in parsing and generation. The paper argues that by moving from the free monoid over a vocabulary V (standard in formal language theory) to the free group over V, deep affinities between linguistic phenomena and classical algebra come to the surface, and that the consequences of tapping the mathematical connections thus established can be considerable. (shrink)

Medical classification systems aim to provide a manageable taxonomy for sorting diagnoses into their proper classes. The question, this paper wants to critically examine, is how to correctly systematise diseases within classification systems that are applied in a variety of different settings. ICD and DSM , the two major classification systems in medicine and psychiatry, will be the main subjects of this paper; however, the arguments are not restricted to these classification systems but point out general methodological and epistemological challenges (...) of classifying diseases for differing purposes. Deciding what qualifies as a disease to be included into a classification system as well as choosing a specific validator for correctly systematising diseases is complicated because the broad applicability of medical classification systems simultaneously appears as aim and challenge. Drawing upon the case study of classifying Alzheimer’s disease, this paper will address three dilemmas in designing ‘good’ medical classification systems. They are due to general epistemological problems of medicine, such as the relationship between individual manifestations of diseases and the necessity of building groups in order to scientifically elucidate causes of diseases. Moreover, they involve pragmatic issues of designing usable classifications that allow for easily discriminating between classes of diseases, restricting, however, the completeness of disease representations. This paper wants to trace how the choice of certain validators is unavoidably value-laden and deeply intertwined with epistemological assumptions of how different uses relate to each other, resulting either in a prioritisation of (constrained) coherence or of (vague) pluralistic connectibility. (shrink)

In order to apply known general theorems about the effective properties of recursive structures in a particular recursive structure, it is necessary to verify that certain decidability conditions are satisfied. This requires the determination of when certain relations, called back and forth relations, hold between finite strings of elements from the structure. Here we determine this for recursive reduced abelian p-groups, thus enabling us to apply these theorems.

In constructive mathematics it is of interest to consider a more general, but classically equivalent, notion of linear order, a so-called pseudo-order. The prime example is the order of the constructive real numbers. We examine two kinds of constructive completions of pseudo-orders: order completions of pseudo-orders and Cauchy completions of ordered groups and fields. It is shown how these can be predicatively defined in type theory, also when the underlying set is non-discrete. Provable choice principles, in particular a (...) generalisation of dependent choice, are used for showing set-representability of cuts. (shrink)

The following two assertions are equivalent for an o-minimal expansion of an ordered group $$\mathcal M=(M,<,+,0,\ldots )$$. There exists a definable bijection between a bounded interval and an unbounded interval. Any definable continuous function $$f:A \rightarrow M$$ defined on a definable closed subset of $$M^n$$ has a definable continuous extension $$F:M^n \rightarrow M$$.

An exponential $\exp $ on an ordered field $$. The structure $$ is then called an ordered exponential field. A linearly ordered structure $$ is called o-minimal if every parametrically definable subset of M is a finite union of points and open intervals of M.The main subject of this thesis is the algebraic and model theoretic examination of o-minimal exponential fields $$ whose exponential satisfies the differential equation $\exp ' = \exp $ with initial condition $\exp = (...) 1$. This study is mainly motivated by the Transfer Conjecture, which states as follows:Any o-minimal exponential field $$ whose exponential satisfies the differential equation $\exp ' = \exp $ with initial condition $\exp =1$ is elementarily equivalent to $\mathbb {R}_{\exp }$.Here, $\mathbb {R}_{\exp }$ denotes the real exponential field $$, where $\exp $ denotes the standard exponential $x \mapsto \mathrm {e}^x$ on $\mathbb {R}$. Moreover, elementary equivalence means that any first-order sentence in the language $\mathcal {L}_{\exp } = \{+,-,\cdot,0,1, <,\exp \}$ holds for $$ if and only if it holds for $\mathbb {R}_{\exp }$.The Transfer Conjecture, and thus the study of o-minimal exponential fields, is of particular interest in the light of the decidability of $\mathbb {R}_{\exp }$. To the date, it is not known if $\mathbb {R}_{\exp }$ is decidable, i.e., whether there exists a procedure determining for a given first-order $\mathcal {L}_{\exp }$ -sentence whether it is true or false in $\mathbb {R}_{\exp }$. However, under the assumption of Schanuel’s Conjecture—a famous open conjecture from Transcendental Number Theory—a decision procedure for $\mathbb {R}_{\exp }$ exists. Also a positive answer to the Transfer Conjecture would result in the decidability of $\mathbb {R}_{\exp }$. Thus, we study o-minimal exponential fields with regard to the Transfer Conjecture, Schanuel’s Conjecture, and the decidability question of $\mathbb {R}_{\exp }$.Overall, we shed light on the valuation theoretic invariants of o-minimal exponential fields—the residue field and the value group—with additional induced structure. Moreover, we explore elementary substructures and extensions of o-minimal exponential fields to the maximal ends—the smallest elementary substructures being prime models and the maximal elementary extensions being contained in the surreal numbers. Further, we draw connections to models of Peano Arithmetic, integer parts, density in real closure, definable Henselian valuations, and strongly NIP ordered fields.Parts of this thesis were published in [2–5].Abstract prepared by Lothar Sebastian KrappE-mail: [email protected]: https://d-nb.info/1202012558/34. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. David Elohim examines the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable (...) propositions, and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal and hyperintensional cognitivism and modal and hyperintensional expressivism. Elohim develops a novel, topic-sensitive truthmaker semantics for dynamic epistemic logic, and develops a novel, dynamic two-dimensional semantics grounded in two-dimensional hyperintensional Turing machines. Chapter \textbf{3} provides an abstraction principle for two-dimensional (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} is availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between Elohim's hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. Elohim countenances a hyperintensional semantics for novel epistemic abstractionist modalities. Elohim suggests, too, that higher observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for two-dimensional hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between interpretational and objective modalities and the truthmakers thereof. This yields the first hyperintensional category theory in the literature. Elohim invents a new mathematical trick in which first-order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals in the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Elohim provides a counter-example to epistemic closure for logical deduction. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

Decidability of monadic first-order classical logic was established by Löwenheim in 1915. The proof made use of a semantic argument and a purely syntactic proof has never been provided. In the present paper we introduce a syntactic proof of decidability of monadic first-order logic in innex normal form which exploits G3-style sequent calculi. In particular, we introduce a cut- and contraction-free calculus having a (complexity-optimal) terminating proof-search procedure. We also show that this logic can be faithfully embedded in (...) the modal logic T. (shrink)

Let $L = \langle, +, h_q, 1\rangle_{q \in \mathbb{Q}}$ where $\mathbb{Q}$ is the set of rational numbers and $h_q$ is a one-place function symbol corresponding to multiplication by $q$. Then the $L$-theory of Scott's model for intuitionistic analysis is decidable.

We show that if H is an effectively completely decomposable computable torsion-free abelian group, then there is a computable copy G of H such that G has computable orders but not orders of every degree.

Background: Providing oncological care to children is demanding and ethical issues concerning what is best for the child can contribute to moral distress. Objectives: To explore healthcare professionals’ experiences of situations that generate moral distress in Swedish paediatric oncology. Research design: In this national study, data collection was conducted using the Swedish Moral Distress Scale-Revised. The data analysis included descriptive statistics and non-parametric analysis of differences between groups. Participants and research context: Healthcare professionals at all paediatric oncology centres in (...) Sweden were invited to participate. A total of 278 healthcare professionals participated. The response rate was 89%. Ethical considerations: In its advisory statement, the Regional Ethical Review Board decided that the study was of such a nature that the legislation concerning ethical reviews was not applicable. All participants received written information about the aim of the study and confidentiality. Participants demonstrated their consent by returning the survey. Findings: The two situations with the highest moral distress scores concerned lack of competence and continuity of personnel. All professional groups reported high levels of disturbance. Nurses rated significantly higher frequencies and higher total Moral Distress Scale scores compared to medical doctors and nursing assistants. Discussion: Lack of competence and continuity, as the two most morally distressing situations, confirms the findings of studies from other countries, where inadequate staffing was reported as being among the top five morally distressing situations. The levels of total Moral Distress Scale scores were more similar to those reported in intensive care units than in other paediatric care settings. Conclusion: The two most morally distressing situations, lack of competence and continuity, are both organisational in nature. Thus, clinical ethics support services need to be combined with organisational improvements in order to reduce moral distress, thereby maintaining job satisfaction, preventing a high turnover of staff and ensuring the quality of care. (shrink)

The aim of this paper is to give a new proof for the decidability and finite model property of first-order logic with two variables (without function symbols), using a combinatorial theorem due to Herwig. The results are proved in the framework of polyadic equality set algebras of dimension two (Pse 2 ). The new proof also shows the known results that the universal theory of Pse 2 is decidable and that every finite Pse 2 can be represented on a (...) finite base. Since the class Cs 2 of cylindric set algebras of dimension 2 forms a reduct of Pse 2 , these results extend to Cs 2 as well. (shrink)

BackgroundHealth decisions occur in a context with omnipresent social influences. Information concerning what other patients decide may present certain interventions as more desirable than others.ObjectivesTo explore how physicians refer to what other people decide in conversations about the relevancy of cardio-pulmonary resuscitation or do-not-attempt-resuscitation orders.MethodsWe recorded forty-three physician–patient admission interviews taking place in a hospital in French-speaking Switzerland, during which CPR is discussed. Data was analysed with conversation analysis.ResultsReference to what other people decide in regards to CPR is used five (...) times, through reported speech. The reference is generic, and employed as a resource to deal with trouble encountered with the patient’s preference, either because it is absent or potentially incompatible with the medical recommendation. In our data, it is a way for physicians to present decisional paths and to steer towards the relevancy of DNAR orders. By calling out to a sense of membership, it builds towards the patient embracing norms that are associated with a desirable or relevant social group.ConclusionsIntroducing DNAR decisions in terms of what other people opt for is a way for physicians to bring up the eventuality of allowing natural death in a less overt way. Formulating treatment choices in terms of what other people do has implications in terms of supporting autonomous and informed decision making, since it nudges patients towards conformity with what is presented as the most preferable choice on the basis of social norms. (shrink)

In this paper, I address a question in social epistemology about the unity of a scientic community to- wards its inner groups (teams, labs...). I investigate the reasons why these groups might want to \go it alone", working among themselves and hiding their discoveries from other groups. I concentrate on the intermediate results of a longer project, where the first steps can help to achieve a more advanced result. I study to what extent the isolation of research (...) groups might be damaging to the epistemic progress of the whole community. In order to get an idea of the reason why scientists might not share their intermediate results with others, consider for example Schawlow and Townes in the summer of 1958 (the historical material is drawn from Broberg, 1991, chap. 3): together they had just designed the principle of functioning of what would be known as the laser, with the intention of constructing the rst laser, relying on their theoretical ideas. Should they have published their theoretical discovery, or rather taken advantage of their advance on possible oppo- nents and start the experimental work? They chose to publish their theoretical ideas in a scientic journal, and they also led a patent application. On the one hand, it was a valuable choice: the patent was granted and their paper was published, making them soon famous. Further- more, another scientist called Gould was to le a simi- lar patent application a few months later, in March 1959; it was refused, because of the priority of Schawlow and Townes. If the latter had not submitted their idea in 1958, the patent would certainly have been acknowl- edged to Gould. In this sense, publishing their intermediate result was a worthy strategy. On the other hand, history showed that their publication had also some drawbacks for them. Schawlow and Townes' publication triggered a race among many American laboratories for the rst experimental construction of the laser. In addition to bringing them competitors, their publication helped these competitors in crucial ways; so much so that it was another scientist, Maiman, and not Schawlow and Townes, who was able to build the rst working laser, in May 1960, and to publish the result. If Schawlow and Townes had not published their theoretical idea, there are chances that they would have been the first ones to build a laser. Their publication of the first theoretical result certainly prevented them from getting the second experimental one. In short, the best publishing strategy about an intermediate result is no easy question for a scientist. Consider now the whole community, concerned with the results available to all and with the pace of the epistemic progress. Schawlow and Townes' publication enabled the rst laser to be built quicker, as other teams could rely on their theoretical work. More generally, being able to reuse other's works seems to be a rm basis of scientic progress. Thus, for the whole community, it seems that there are only benets if intermediate results are published. As this is not necessarily the best strategy for those who reach these intermediate results, there might be a conflict between the interests of individuals and those of the whole community. The question Schawlow and Townes faced was whether they should make their discovery publicly known, or keep it for themselves to progress alone. This alternative can also arise for an entire lab, when competing with other labs on some long-run project: should it make its discoveries known to its opponents, or only share them internally among its members? At a higher level still, this question arises for what can be called scientic schools, which are groups of labs sharing some particular approach|methodological, experimental or interpre- tational, for example. At each level within the scientic community, there are competitive groups of scientists which may decide to go it alone and to prevent their results from being accessible to others. If they had good reasons for doing so, there would be dramatic consequences for the whole community: other groups would not be able to reuse their results, labour force would be wasted in achieving them again, and the progress of the eld would be slowered. 9 The aim of this paper is to investigate this risk of division: to assess the conditions under which it may oc- cur, its damage for the community, and to draw the limit of an acceptable pluralism. The reasoning with benets and drawbacks which has been sketched for Schawlow and Townes seems to be implicitly an informal economic argument. In order to clarify and to rene such an argument, I will investigate it in a rational decision framework, supposing some utility or preferences for the groups of scientists, and I will propose a formal model, in game theory. In social epistemology of science, formal models have been proposed for various questions (for example, Kitcher 1990, 1993, Goldman 2009, Strevens 2003, 2006, Weisberg and Muldoon, forthcoming, Zollman 2007, 2008, 2009, 2010), but not for the question of the division of the scientic community. I will concentrate on the normative aspect of the question, ignoring the descriptive and historical question of whether groups do go it alone or not. The model I propose is sequential: two groups are competing on a research program, which consists of several results which have to be obtained in order. The groups always carry out some research for the next result, which they reach with some probability per unit of time. When a group, say A, reaches a result, it can either make it public for the other group, or continue its research. After a result is made public, the competitor B can start from it so as to continue its own research. Thus, when A publishes it loses its lead, and its competitor will be able to compete with it in the near future. But it is also recognized as the rst to reach this step. I consider two dierent cases, one in which the number of steps is limited, another where the limit concerns the number of temporal intervals. In both cases, assuming that all steps are equally dicult and equally rewarding, it turns out that the best strategy for a group concerned with its own reward is to make public every step it takes. Thus, there is no risk that groups might separate: a scientist, whatever its group, will publish for all. Finally, I turn to more complex situations, where results have varying size or diculty: there, groups can indeed be better o going it alone. (shrink)

The fundamental question in reverse mathematics is to determine which set existence axioms are required to prove particular theorems of mathematics. In addition to being interesting in their own right, answers to this question have consequences in both effective mathematics and the foundations of mathematics. Before discussing these consequences, we need to be more specific about the motivating question.Reverse mathematics is useful for studying theorems of either countable or essentially countable mathematics. Essentially countable mathematics is a vague term that is (...) best explained by an example. Complete separable metric spaces are essentially countable because, although the spaces may be uncountable, they can be understood in terms of a countable basis. Simpson gives the following list of areas which can be analyzed by reverse mathematics: number theory, geometry, calculus, differential equations, real and complex analysis, combinatorics, countable algebra, separable Banach spaces, computability theory, and the topology of complete separable metric spaces. Reverse mathematics is less suited to theorems of abstract functional analysis, abstract set theory, universal algebra, or general topology.Section 2 introduces the major subsystems of second order arithmetic used in reverse mathematics: RCA0, WKL0, ACA0, ATR0 and – CA0. Sections 3 through 7 consider various theorems of ordered group theory from the perspective of reverse mathematics. Among the results considered are theorems on ordered quotient groups, groups and semigroup conditions which imply orderability, the orderability of free groups, Hölder's Theorem, Mal'tsev's classification of the order types of countable ordered groups. (shrink)

We study Dedekind cuts on ordered Abelian groups. We introduce a monoid structure on them, and we characterise, via a suitable representation theorem, the universal part of the theory of such structures.

This paper investigates the “general” semantics for first-order logic introduced to Antonelli, 637–58, 2013): a sound and complete axiom system is given, and the satisfiability problem for the general semantics is reduced to the satisfiability of formulas in the Guarded Fragment of Andréka et al. :217–274, 1998), thereby showing the former decidable. A truth-tree method is presented in the Appendix.

A totally ordered group G is essentially periodic if for every definable non-trivial convex subgroup H of G every definable subset of G is equal to a finite union of cosets of subgroups of G on some interval containing an end segment of H; it is coset-minimal if all definable subsets are equal to a finite union of cosets, intersected with intervals. We study definable sets and functions in such groups, and relate them to the quasi-o-minimal groups (...) introduced in Belegradek et al. . Main results: An essentially periodic group G is abelian; if G is discrete, then definable functions in one variable are ultimately piecewise linear. A group such that every model elementarily equivalent to it is coset-minimal is quasi-o-minimal , and its definable functions in one variable are piecewise linear. (shrink)

Regarding strictly monadic second‐order logic (SMSOL), which is the fragment of monadic second‐order logic in which all predicate constants are unary and there are no function symbols, we show that a standard deductive system with full comprehension is sound and complete with respect to standard semantics. This result is achieved by showing that in the case of SMSOL, the truth value of any formula in a faithful identity‐standard Henkin structure is preserved when the structure is “standardized”; that is, the predicate (...) domain is expanded into the set of all unary relations. In addition, we obtain a simpler proof of the decidability of SMSOL. (shrink)

In order responsibly to decide whether there ought to be an international legal right of secession, I believe we need an account of the morality of secession. I propose that territorial and political societies have a moral right to secede, and on that basis I propose a regime designed to give such groups an international legal right to secede. This regime would create a procedure that could be followed by groups desiring to secede or by states desiring to (...) resolve the issue of secession. It would give territorial political societies a legally recognized liberty to conduct a plebiscite on secession, and, assuming such a plebiscite is won by the secessionist side, a qualified right in international law to create a state without interference. Alan Buchanan has argued that proposals of this sort would create perverse incentives. I argue that there is no good reason to believe this. The point is to allow the legal regulation of secession in cases where there are active secessionist movements with legitimate moral claims, and to attempt to dampen the desire for secession in cases where secessionist sentiment is not well grounded in social and geographic reality. (shrink)

We present a logic which we call Hybrid Duration Calculus. HDC is obtained by adding the following hybrid logical machinery to the Restricted Duration Calculus : nominals, satisfaction operators, down-arrow binder, and the global modality. RDC is known to be decidable, and in this paper we show that decidability is retained when adding the hybrid logical machinery. Decidability of HDC is shown by reducing the satisfiability problem to satisfiability of Monadic Second-Order Theory of Order. We illustrate the increased (...) expressive power obtained in hybridizing RDC by showing that HDC, in contrast to RDC, can express all of the 13 possible relations between intervals. (shrink)

This study aimed to investigate whether the ordinal judgments of high math-anxious and low math-anxious individuals differ. Two groups of 20 participants with extreme scores on the Shortened Mathematics Anxiety Rating Scale had to decide whether a triplet of numbers was presented in ascending order. Triplets could contain one-digit or two-digit numbers and be formed by consecutive numbers, numbers with a constant distance of two or three or numbers with variable distances between them. All these triplets were also presented (...) unordered: sequence order in these trials could be broken at the second or third number. A reverse distance effect of equal size was found in both anxiety groups. However, HMA participants made more judgment errors than their LMA peers when they judged one-digit counting ordered triplets. This effect was related to worse performance of HMA individuals on a symmetry span test and might be related to group differences on working memory. Importantly, HMAs were less accurate than LMA participants at rejecting unordered D2 sequences. This result is interpreted in terms of worse cognitive flexibility in HMA individuals. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Annual Meeting of the Society for Buddhist-Christian Studies:Atlanta, Georgia, USA, 29-30 October 2010Sandra Costen KunzThis past fall the Society for Buddhist-Christian Studies (SBCS) presented two sessions at the annual meeting of the American Academy of Religion (AAR) in Atlanta, Georgia. On Friday afternoon, 29 October, an extremely well-attended and in many ways inspiring session titled "The Scholarly Contributions of Rita M. Gross" was presented. The second panel, titled (...) "Can/Should Buddhists and Christians Do Theology/ Buddhology Together?" was presented on Saturday morning, 30 October. It also drew a considerable crowd.Each of the six members of Friday's panel addressed a different aspect of the work of Rita Gross, longtime SBCS leader and now professor emerita of comparative studies in religion, University of Wisconsin-Eau Claire. She is also a senior teacher (lopon) in Jetsun Khandro Rinpoche's U.S. Lotus Garden center. The session was organized and moderated by current SBCS president Miriam M. Levering, professor of religious studies and Asian studies at University of Tennessee, Knoxville, and an international advisor at Rissho Ko-Sekei in Tokyo. I will give highlights from the panelists' presentations in the order in which they spoke.Kathleen Erndl, associate professor of religion at Florida State University, focused on Gross's work as teacher and mentor. Although she taught primarily undergraduates, Gross, in her writing, speaking, and generous conversation with rising scholars, not only moved the field toward taking religious practices and women's religious experience more seriously but also had a huge influence on how "women in religion" is taught. Gross was one of the first scholars to use the term "androcentric." Nancy Auer Falk, professor emerita of comparative religion at Western Michigan University, coedited Unspoken Worlds: Women's Religious Lives (1981) with Gross. Now in its third edition, this groundbreaking collection of case studies watered the flowering of cross-cultural studies in the lived religion of women. Falk reminded us of Gross's role in the election of the first female member of the AAR's board and the establishment of its working group on women and religion. Judith Simmer-Brown, professor of religious [End Page 221] studies at Naropa University, focused on Gross's work in Tibetan Buddhist studies, especially her pointing out the discrepancy between the prophetic voices about women's roles in early Buddhist texts and Tibetan monasticism's institutionalized androcentrism. Simmer-Brown emphasized the importance of Gross's work in Buddhist theology—for example, her deconstructing "Theravada/Mahayana/Vajrayana put-downs" and "incipient fundamentalisms" in Western Buddhism.The fourth panelist, Paul F. Knitter, professor of theology, world religions, and culture at Union Theological Seminary, described Gross's contributions to Buddhist-Christian dialogue, recounting that they met at the Society's founding conference in 1980. He said, "Rita is the Christian theologians' friendly gadfly, always asking questions that make us very uncomfortable." Particularly provocative has been her insistence that claims on the part of religious communities to religious superiority or exclusive truth are incompatible with support of religious diversity. SBCS vice president Terry Muck, dean of the E. Stanley Jones School of World Mission and Evangelism at Asbury Theological Seminary, spoke about Gross's contributions to the society, noting that she has held every office except treasurer. He and Gross coedited Buddhist-Christian Studies from 1995-2005, in part because the society had decided— after founding editor David Chappell retired—that the ideal would be one male and one female editor and one Buddhist and one Christian editor. He usually handled the work with the publisher while she usually worked with article selection along with the reviewers. Rosemary Radford Ruether, professor emerita at the Pacific School of Religion, reviewed Gross's contributions to feminist scholarship. She reminded us that while still a student at the University of Chicago, Gross crafted a fundamental methodology for studying women and religion and insisted that turning a blind eye to 80 percent of the religious practice in various cultures is simply bad empiricism. Gross has consistently pointed out that colonialism is connected with privileging males and texts, Reuther claimed, and that no one studies religion with "objectivity."Gross's response to these presentations focused on... (shrink)

We study theorems of ordered groups from the perspective of reverse mathematics. We show that suffices to prove Hölder's Theorem and give equivalences of both (the orderability of torsion free nilpotent groups and direct products, the classical semigroup conditions for orderability) and (the existence of induced partial orders in quotient groups, the existence of the center, and the existence of the strong divisible closure).