Here we work in an arbitrary o-minimal expansion of a divisible ordered abelian group. We say that a definable ring is definably semiprime if squares of nontrivial two-sided ideals definable in the expansion are nontrivial. We prove a definable version of Wedderburn–Artin theorem and give a characterization of definably semiprime rings.

The aim of this manuscript is to introduce the \((\alpha,\beta)\)-hesitant fuzzy set and apply it to semigroups. In this paper, as a generalization of the concept of hesitant fuzzy sets to semigroup theory, the concept of \((\alpha,\beta)\)-hesitant fuzzy subsemigroups of semigroups is introduced, and related properties are discussed. Furthermore, we define and study \((\alpha,\beta)\)-hesitant fuzzy ideals on semigroups. In particular, we investigate the structure of \((\alpha,\beta)\)-hesitant fuzzy ideal generated by a hesitant fuzzy ideal in a semigroup. In addition, we also (...) introduce the concepts of \((\alpha,\beta)\)-hesitant fuzzy semiprime sets of semigroups, and characterize regular semigroups in terms of \((\alpha,\beta)\)-hesitant fuzzy left ideals and \((\alpha,\beta)\)-hesitant fuzzy right ideals. Finally, several characterizations of regular and intra-regular semigroups by the properties of \((\alpha,\beta)\)-hesitant ideals are given. (shrink)

We prove an analogue of the fixed-point theorem for the case of definably amenable groups.

Without doubt, terrorism is one of the most vehemently debated subjects in current political affairs as well as in academic discourse. Yet, although it constitutes an issue of general socio-political interest, neither in everyday language nor in professional (political, legal, or academic) contexts does there exist a generally accepted definition of terrorism. The question of how it should be defined has been answered countless times, with as much variety as quantity in the answers. In academic discourse, it is difficult to (...) find two scholars who use the term ‘terrorism’ in the same way. -/- While it is impossible to formulate a definition which satisfies everyone, discussing the definition question is indispensable. The necessity to review existing definitions with a view to improving them is especially obvious in legal and political contexts. How terrorism is defined in these contexts has serious consequences, and if we lack clear definitions we run into problems. How can we have laws or take political measures against something we have not clearly defined? Without doubt, there exists a practical necessity for a definition in these fields. It is important to have clear standards for defining terrorism. -/- In my view, the definition should meet three basic criteria: first, it should cover those cases that we concurrently consider to be instances of terrorism (such as the attacks on the World Trade Center in New York and the Pentagon in September 2001 or those on commuting trains in Madrid Atocha in March 2004). That is, ideally, our definition of terrorism remains close to uncontroversial usages of the term. Second, the definition should abstain from morally judging the act in question. Later I will say more about so called “moral” definitions of terrorism. For now, it suffices to say that defining an action and evaluating it are distinct tasks and should remain so. Third, the definition must identify characteristics that are specific to terrorism alone, characteristics which clearly distinguish it from other phenomena. (shrink)

Both the Beth definability theorem and Craig's lemma (interpolation theorem from now on) deal with the issue of the entanglement of one language L1 with another language L2, that is to say, information transfer—or the lack of such transfer—between the two languages. The notion of splitting we study below looks into this issue. We briefly relate our own results in this area as well as the results of other researchers like Kourousias and Makinson, and Peppas, Chopra and Foo.Section 3 does (...) contain one apparently new theorem. (shrink)

An argument of A. Borel [Bor—61, Proposition 3.1] shows that every compact connected Lie group is homeomorphic to the Cartesian product of its derived subgroup and a torus. We prove a parallel result for definably compact definably connected groups definable in an o-minimal expansion of a real closed field. As opposed to the Lie case, however, we provide an example showing that the derived subgroup may not have a definable semidirect complement.

We prove that there exists no sentence F of the language of rings with an extra binary predicat I2 satisfying the following property: for every definable set X ⊆ ℂ2, X is connected if and only if ⊧ F, where I2 is interpreted by X. We conjecture that the same result holds for closed subset of ℂ2. We prove some results motivated by this conjecture.

We give two theories, Th1 and Th2, which are explicitly definable over each other , but are not definitionally equivalent. The languages of the two theories are disjoint.

We study connections between asymptotic structure in a Banach space and model theoretic properties of the space. We show that, in an asymptotic sense, a sequence $$ in a Banach space X generates copies of one of the classical sequence spaces $\ell_p$ or $c_0$ inside X if and only if the quantifier-free types approximated by $$ inside X are quantifier-free definable. More precisely, if $$ is a bounded sequence X such that no normalized sequence of blocks of $$ converges, then (...) the following two conditions are equivalent. There exists a sequence $$ of blocks of $$ such that for every finite dimensional subspace E of X, every quantifier-free type over $E +\overline{\rm span}\{y_n\mid n\in \mathbb{N}\}$ is quantifier-free definable. One of the following two conditions holds: there exists $1\le p 0$ and every finite dimensional subspace E of X there exists a sequence of blocks of $$ which is $$-equivalent over E to the standard unit basis of $\ell_p$; for every $\epsilon>0$ and every finite dimensional subspace E of X there exists a sequence of blocks of $$ which is $$-equivalent over E to the standard unit basis of $c_0$. Several byproducts of the proof are analyzed. (shrink)

The paper generalises Goldblatt's completeness proof for Lemmon–Scott formulas to various modal propositional logics without classical negation and without ex falso, up to positive modal logic, where conjunction and disjunction, andwhere necessity and possibility are respectively independent.Further the paper proves definability theorems for Lemmon–Scottformulas, which hold even in modal propositional languages without negation and without falsum. Both, the completeness theorem and the definability theoremmake use only of special constructions of relations,like relation products. No second order logic, no general frames are (...) involved. (shrink)

We show that type-definable subgroups of measure algebras are definable.

Let K be an infinite Galois extension of the rationals such that every finite subextension has odd degree over the rationals and its prime ideals dividing 2 are unramified. We show that its ring of integers is first-order definable in K. As an application we prove that equation image together with all its Galois subextensions are undecidable, where Δ is the set of all the prime integers which are congruent to −1 modulo 4.

The concept of moral distress comes from nursing ethics, and was initially defined as ‘…when one knows the right thing to do, but institutional constraints make it nearly impossible to pursue the right course of action’. There is a large body of literature associated with moral distress, yet multiple definitions now exist, significantly limiting its usefulness. We undertook a systematic review of the argument-based bioethics literature on this topic as the basis for a critical appraisal, identifying 55 papers for analysis. (...) We found that moral distress is most frequently framed around individual experiences of distress in relation to local practices and constraints, and understood in terms of power relations and workplace hierarchies. This understanding is directly derived from, and often still seen as specific to, nursing. Frequently the perspective of the morally distressed individual is privileged. Understandings of moral distress have evolved towards an ‘occupational health approach’, with the assumption that moral distress should be measured and prevented. Counter-perspectives were identified, highlighting conceptual problems. Based on our review, we propose a redefinition of moral distress: ‘Ethical unease or disquiet resulting from a situation where a clinician believes they have contributed to avoidable patient or community harm through their involvement in an action, inaction or decision that conflicts with their own values’. This definition is specific enough for research use, anchored in clinicians’ professional responsibilities and concerns about harms to patients, framed relationally rather than hierarchically, and amenable to multiple perspectives on any given morally distressing situation. (shrink)

Niche construction theory (NCT) aims to transform and unite evolutionary biology and ecology. Much of the debate about NCT has focused on construction. Less attention has been accorded to the niche: what is it, exactly, that organisms are constructing? In this paper I compare and contrast the definition of the niche used in NCT with ecological niche definitions. NCT’s concept of the evolutionary niche is defined as the sum of selection pressures affecting a population. So defined, the evolutionary niche is (...) narrower than the ecological niche. Moreover, when contrasted with a more restricted ecological niche concept, it has a slightly different extension. I point out three kinds of cases in which the evolutionary niche does not coincide with realized ecological niches: extreme habitat degradation, commensalism, and non-limiting or super-abundant resources. These conceptual differences affect the role of NCT in unifying ecology and evolutionary biology. (shrink)

We prove that every countable relation on the enumeration degrees, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} ${\frak E}$\end{document}, is uniformly definable from parameters in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} ${\frak E}$\end{document}. Consequently, the first order theory of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} ${\frak E}$\end{document} is recursively isomorphic to the second order theory of arithmetic. By an effective version of coding lemma, we show that the first order (...) theory of the enumeration degrees of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\Sigma^0_2$\end{document} sets is not decidable. (shrink)

Arithmetical definability has been extensively studied over the natural numbers. In this paper, we take up the study of arithmetical definability over finite structures, motivated by the correspondence between uniform AC0 and FO. We prove finite analogs of three classic results in arithmetical definability, namely that < and TIMES can first-order define PLUS, that < and DIVIDES can first-order define TIMES, and that < and COPRIME can first-order define TIMES. The first result sharpens the equivalence FO =FO to FO = (...) FO, answering a question raised by Barrington et al. about the Crane Beach Conjecture. Together with previous results on the Crane Beach Conjecture, our results imply that FO is strictly less expressive than FO = FO = FO. In more colorful language, one could say that, for parallel computation, multiplication is harder than addition. (shrink)

We investigate definable topological dynamics of groups definable in an o‐minimal expansion of the field of reals. Assuming that a definable group G admits a model‐theoretic analogue of Iwasawa decomposition, namely the compact‐torsion‐free decomposition, we give a description of minimal subflows and the Ellis group of its universal definable flow in terms of this decomposition. In particular, the Ellis group of this flow is isomorphic to. This provides a range of counterexamples to a question by Newelski whether the Ellis group (...) is isomorphic to. We further extend the results to universal topological covers of definable groups, interpreted in a two‐sorted structure containing the o‐minimal sort and a sort for an abelian group. (shrink)

Defining Species: A Sourcebook from Antiquity to Today provides excerpts and commentary on the definition of «species from source material ranging from the ...

Let H be an infinite-dimensional (real or complex) Hilbert space, viewed as a metric structure in its natural signature. We characterize the definable linear operators on H as exactly the "scalar plus compact" operators.

ABSTRACT In recent years there has been intense debate regarding the level of medical care provided to ‘standard care’ control groups in clinical trials in developing countries, particularly when the research sponsors come from wealthier countries. The debate revolves around the issue of how to define a standard of medical care in a country in which many people are not receiving the best methods of medical care available in other settings. In this paper, we argue that additional dimensions of the (...) standard of care have been hitherto neglected, namely, the structure and efficiency of the national health system. The health system affects locally available medical care in two important ways: first, the system may be structured to provide different levels of care at different sites with referral mechanisms to direct patients to the appropriate level of care. Second, inefficiencies in this system may influence what care is available in a particular locale. As a result of these two factors locally available care cannot be equated with a national ‘standard’. A reasonable approach is to define the national standard of care as the level of care that ought to be delivered under conditions of appropriate and efficient referral in a national system. This standard is the minimum level of care that ought to be provided to a control group. There may be additional moral arguments for higher levels of care in some circumstances. This health system analysis may be helpful to researchers and ethics committees in designing and reviewing research involving standard care control groups in developing country research. (shrink)

We define a property R(A 0 , A 1 ) in the partial order E of computably enumerable sets under inclusion, and prove that R implies that A 0 is noncomputable and incomplete. Moreover, the property is nonvacuous, and the A 0 and A 1 which we build satisfying R form a Friedberg splitting of their union A, with A 1 prompt and A promptly simple. We conclude that A 0 and A 1 lie in distinct orbits under automorphisms of (...) E, yielding a strong answer to a question previously explored by Downey, Stob, and Soare about whether halves of Friedberg splittings must lie in the same orbit. (shrink)

The classification of a state of affairs under a legal category can be considered as a kind of con- densed decision that can be made explicit, analyzed, and assessed us- ing argumentation schemes. In this paper, the controversial conflict of opinions concerning the nature of “marriage” in Obergefell v. Hodges is analyzed pointing out the dialecti- cal strategies used for addressing the interpretive doubts. The dispute about the same-sex couples’ right to marry hides a much deeper disa- greement not only (...) about what mar- riage is, but more importantly about the dialectical rules for defining it. (shrink)

We initiate the study of definable [Formula: see text]-topologies and show that there is at most one such [Formula: see text]-topology on a [Formula: see text]-henselian NIP field. Equivalently, we show that if [Formula: see text] is a bi-valued NIP field with [Formula: see text] henselian, then [Formula: see text] and [Formula: see text] are comparable. As a consequence, Shelah’s conjecture for NIP fields implies the henselianity conjecture for NIP fields. Furthermore, the latter conjecture is proved for any field admitting (...) a henselian valuation with a dp-minimal residue field. We conclude by showing that Shelah’s conjecture is equivalent to the statement that any NIP field not contained in the algebraic closure of a finite field is [Formula: see text]-henselian. (shrink)

New Blackfriars, Volume 103, Issue 1107, Page 607-621, September 2022.

Given a Henselian valuation, we study its definability (with and without parameters) by examining conditions on the value group. We show that any Henselian valuation whose value group is not closed in its divisible hull is definable in the language of rings, using one parameter. Thereby we strengthen known definability results. Moreover, we show that in this case, one parameter is optimal in the sense that one cannot obtain definability without parameters. To this end, we present a construction method for (...) a t-Henselian non-Henselian ordered field elementarily equivalent to a Henselian field with a specified value group. (shrink)

A set F of Boolean functions is said to be functionally complete if every Boolean function is definable by combining functions in F. Post clarified when a set of Boolean functions is functionally complete (with respect to classical semantics). In this paper, by extending Post’s theorem, we clarify when a set of Boolean functions is functionally complete with respect to Kripke semantics.

Background: Compassion has long been advocated as a fundamental element in nursing practice and education. However, defining and translating compassion into caring practice by nursing students who are new to the clinical practice environment as part of their educational journey remain unclear. Objectives: The aim of this study was to explore how Chinese baccalaureate nursing students define and characterize compassionate care as they participate in their clinical practice. Methods: A descriptive qualitative study design was used involving a semi-structured in-depth interview (...) method and qualitative content analysis. Twenty senior year baccalaureate nursing students were interviewed during their clinical practicum experience at four teaching hospitals. Ethical considerations: Permission to conduct the study was received from the Institutional Review Boards and the participating hospitals. Results: Baccalaureate nursing students defined and characterized compassionate care as a union of “empathy” related to a nurse’s desire to “alleviate patients’ suffering,” “address individualized care needs,” “use therapeutic communication,” and “promote mutual benefits with patients.” Students recognized that the “practice environment” was characterized by nurse leaders’ interpersonal relations, role modeling by nurses and workloads which influenced the practice of compassionate care by nursing personnel. Conclusion: Compassionate care is crucial for patients, nurses, and students in their professional development as well as the development of the nursing profession. In order to provide compassionate care, a positive practice environment promoted by hospital administrators is needed. This also includes having an adequate workforce of nurses who can role model compassionate care to students in their preceptor role while meeting the needs of their patients. (shrink)

We show that the e-degree 0'e and the map u ↦ u' are definable in the upper semilattice of all e-degrees. The class of total e-degrees ≥0'e is also definable.

We study the flow of trigonalizable algebraic group acting on its type space, focusing on the problem raised in [17] of whether weakly generic types coincide with almost periodic types if the group has global definable f‐generic types, equivalently whether the union of minimal subflows of a suitable type space is closed. We shall give a description of f‐generic types of trigonalizable algebraic groups, and prove that every f‐generic type is almost periodic.

We study the question of $\mathcal {L}_{\mathrm {ring}}$ -definability of non-trivial henselian valuation rings. Building on previous work of Jahnke and Koenigsmann, we provide a characterization of henselian fields that admit a non-trivial definable henselian valuation. In particular, we treat the cases where the canonical henselian valuation has positive residue characteristic, using techniques from the model theory and algebra of tame fields.

We study punctual categoricity on a cone and intrinsically punctual functions and obtain complete structural characterizations in terms of model-theoretic notions. As a corollary, we answer a question of Bazhenov, Downey, Kalimullin, and Melnikov by showing that relational structures are not punctually universal. We will also apply this characterisation to derive an algebraic characterisation of relatively punctually categorical mono-unary structures.

We give a definition, in the ring language, of Zp inside Qp and of Fp[[t]] inside Fp), which works uniformly for all p and all finite field extensions of these fields, and in many other Henselian valued fields as well. The formula can be taken existential-universal in the ring language, and in fact existential in a modification of the language of Macintyre. Furthermore, we show the negative result that in the language of rings there does not exist a uniform definition (...) by an existential formula and neither by a universal formula for the valuation rings of all the finite extensions of a given Henselian valued field. We also show that there is no existential formula of the ring language defining Zp inside Qp uniformly for all p. For any fixed finite extension of Qp, we give an existential formula and a universal formula in the ring language which define the valuation ring. (shrink)

The quality of a research study application sends a distinct signal to the institutional review board (IRB) about the skills, capacities, preparation, communication, experience, and resources of its authors. However, efforts to research and define IRB application quality have been insufficient. Inattention to the quality of an IRB application is consequential because the application precedes IRB review, and perceptions of quality between the two may be interrelated and interdependent. Without a clear understanding of quality, IRBs do not know how to (...) define quality and researchers do not know how to achieve quality. This position has not been systematically studied to date, and future research could provide much-needed empirical validation. This paper lays the conceptual groundwork for future investigation into what constitutes quality in an IRB application. It includes a landscape review of multidisciplinary research on quality, as well as a discussion of quality frameworks analogous to research with human participants that exist in the published literature. It also examines the background and significance of federal research regulations, regulatory burdens, researchers’ regulatory literacy, and the roles and responsibilities of IRB professionals within this ecosystem. (shrink)

We give an example of a structure equation image on the real line, and a manifold M definable in equation image, such that M is definably connected but is not connected.

We prove that every type of finite Cantor-Bendixson rank over a model of a first-order theory without the strict order property is definable and has a unique nonforking extension to a global type. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

At first glance, atheism seems simple to define. If atheism is the negation of theism, and if theism is the view that at least one god exists, then atheism is the negation of this view. However, the common definitions that follow from this insight suffer from two problems: first, they often leave undefined what “god” means, and, second, they understate the scope of the disagreement between theists and atheists, which often has as much to do with the fundamental character of (...) reality as with the existence of one being in it. Some writers address the second problem by reinterpreting atheism as the logical consequence of particular metaphysical views, such as naturalism or physicalism, which are then taken as the true meaning of atheism. These interpretations, though more satisfactory in some respects, can result in concepts of atheism that are unclear or too narrow, and they often still leave “god” undefined. In this paper, I propose that atheism be defined as the proposition that reality is solely an impersonal order. Theism is the proposition that reality is not solely an impersonal order, being either a personal order, that is, an order founded by at least one person, or an impersonal order plus at least one transcendent person. A god is a person who is not subject to the laws governing that order and thus transcends it. I explain these definitions and briefly discuss some of their implications. First I survey prior definitions of atheism to display the problems they raise. (shrink)

There has been much debate among scientists and philosophers about what it means for interventions invoked in causal inference to be “well-defined” and how considerations of this sort should constrain the choice of causal variables. In this paper, I propose that an intervention is well-defined just in case the effect of interest is well-defined, and that the intervention can serve as a suitable means to identify that effect. Based on this proposal, I identify several types of ambiguous intervention. Implications for (...) variable choice are discussed using case studies drawn from the sciences. (shrink)

Assume [Formula: see text]. Let [Formula: see text] be a [Formula: see text] equivalence relation coded in [Formula: see text]. [Formula: see text] has an ordinal definable equivalence class without any ordinal definable elements if and only if [Formula: see text] is unpinned. [Formula: see text] proves [Formula: see text]-class section uniformization when [Formula: see text] is a [Formula: see text] equivalence relation on [Formula: see text] which is pinned in every transitive model of [Formula: see text] containing the real (...) which codes [Formula: see text]: Suppose [Formula: see text] is a relation on [Formula: see text] such that each section [Formula: see text] is an [Formula: see text]-class, then there is a function [Formula: see text] such that for all [Formula: see text], [Formula: see text]. [Formula: see text] proves that [Formula: see text] is Jónsson whenever [Formula: see text] is an ordinal: For every function [Formula: see text], there is an [Formula: see text] with [Formula: see text] in bijection with [Formula: see text] and [Formula: see text]. (shrink)

The concept of medical necessity plays a central role in many healthcare systems, including Canada's, by helping determine which healthcare services will receive funding. Despite its significance in health policy frameworks, medical necessity has proven to be notoriously difficult to define and operationalise. A shift toward a more personalised and genetically‐informed approach to the provision of healthcare seems likely to heighten associated policy challenges. One of the stated goals of personalised medicine is to save healthcare systems money by facilitating the (...) use of less and more effective treatments. However, any cost saving potential may ultimately be thwarted by physicians' legal and ethical obligations, given that physicians will inevitably be required to implement and define the bounds of genetically‐informed medical necessity for their patients. (shrink)

Stalnaker (_Context_, Oxford University Press, Oxford, 2014) defends two ideas about common ground. The first is that the common ground of a conversation is definable in terms of an iterated propositional attitude of _acceptance_, so that _p_ is common ground iff _p_ is commonly accepted. The second is the idea that the “default setting" of conversational acceptance is belief, so that as a default, what is accepted in conversation coincides with what is (commonly) believed. In this paper, I argue that (...) we should favor a pair of contrasting theses instead. First, I argue that we should identify the common ground with what is common knowledge about what is accepted, so that _p_ is common ground iff it is common knowledge that _p_ is accepted. Thus the attitude that is iterated in the definition of common ground is not acceptance but knowledge. Second, I argue that the “default setting" for conversational acceptance is not belief, but knowledge. (shrink)

Institutional review boards and investigators are used to talking about risks of harm. Both low risks of great harm and high risks of small harm must be disclosed to prospective subjects and should be explained and categorized in ways that help potential subjects to understand and weigh them appropriately. Everyone on an IRB has probably spent time at meetings arguing over whether a three-page bulleted list of risk description is helpful or overkill for prospective subjects. Yet only a small fraction (...) of all the time and attention lavished on risk disclosure has been devoted to discussing whether and when potential benefit to subjects can reasonably be claimed and, if so, how it should be described in the consent form and process.Traditionally, IRBs and regulators have worked to ensure that clear lines can be drawn between research that, by definition, carries no potential for direct benefit — because it uses healthy volunteers or because it is not foreseeably focused on the development of treatments — and research that does have the development of effective treatments as its goal. (shrink)

Zaionc, M., λ-Definability on free algebras, Annals of Pure and Applied Logic 51 279-300. A λ-language over a simple type structure is considered. There is a natural isomorphism which identifies free algebras with nonempty second-order types. If A is a free algebra determined by the signature SA = [α1,...,αn], then by a type τA we mean τ1,...,τn→0 where τi=0αi→0. It can be seen that closed terms of the type τA reflex constructions in the algebra A. Therefore any term of the (...) type n→τA defines some n-ary mapping in algebra A. The problem is to characterize λ-definable mappings in any free algebra. It is proved that the set of λ-definable operations is the minimal set that contains constant functions and projections and is closed under composition and limited recursion. This result is a generalization of the result of Schwichtenberg and Statman which characterize the λ-definable functions over the natural number type →, i.e algebra [1, 0], as well as of the result of Zaionc for λ-definable word operations over type n→, i.e algebra [1,...,1,0], and of the results about λ-definable tree operations , i.e in algebra [2, 0]. Some of the examples in Section 5 are based on a publication of Zaionc. (shrink)

Numerous theories have attempted to overcome the anti-essentialist scepticism about the possibility of defining art. While significant advances have been made in this field, it seems that most modern definitions fail to successfully address the issue of the ever-changing nature of art raised by Morris Weitz, and rarely even attempt to provide an account which would be valid in more than just the modern Western context. This thesis looks at the most successful definitions currently defended, determines their strengths and weaknesses, (...) and offers a new, cultural definition which can preserve the good elements of other theories, solve or avoid their problems, and have a scope wide enough to account for art of different times and cultures. The resulting theory is a synthetic one in that it preserves the essential institutionalism of Dickie's institutional views, is inspired by the historical and functional determination of artistic phenomena present in Levinson's historicism and Beardsley's functionalism, and presents the reasons for something becoming art in a disjunctive form of Gaut's cluster account. Its strengths lie in the ability to account for the changing art-status of objects in various cultures and at various times, providing an explanation of not only what is or was art, but also how and why the concept 'art' changes historically and differs between cultures, and successfully balancing between the over-generalisations of ahistorical and universalist views, and the uninformativeness of relativism. More broadly, the cultural theory stresses the importance of treating art as a historical phenomenon embedded in particular social and cultural settings, and encourages cooperation with other disciplines such as anthropology and history of art. (shrink)

We present a finitary regularly algebraizable logic not finitely equivalential, for every similarity type. We associate to each of these logics a class of algebras with an equivalence relation, with the property that in this class, the identity is atomatically definable but not finitely atomatically definable.

In this paper, using definability of types over indiscernible sequences as a template, we study a property of formulas and theories called "uniform definability of types over finite sets" (UDTFS). We explore UDTFS and show how it relates to well-known properties in model theory. We recall that stable theories and weakly o-minimal theories have UDTFS and UDTFS implies dependence. We then show that all dp-minimal theories have UDTFS.

We study generalized quantifiers on finite structures.With every function : we associate a quantifier Q by letting Q x say there are at least (n) elementsx satisfying , where n is the sizeof the universe. This is the general form ofwhat is known as a monotone quantifier of type .We study so called polyadic liftsof such quantifiers. The particular lifts we considerare Ramseyfication, branching and resumption.In each case we get exact criteria fordefinability of the lift in terms of simpler quantifiers.