In this paper a class of simple theories, called the low theories is developed, and the following is proved. Theorem. Let T be a low theory. A set and a, b elements realizing the same strong type over A. Then, a and b realized the same Lascar strong type over A.

Let T be a countable, small simple theory. In this paper, we prove that for such T, the notion of Lascar strong type coincides with the notion of strong type, over an arbitrary set.

This is an expository note on the Lascar group. We also study the Lascar group over hyperimaginaries and make some new observations on the strong types over those. In particular, we show that in a simple theory $\operatorname{Ltp}\equiv\operatorname{stp}$ in real context implies that for hyperimaginary context.

Although there are important moral arguments against cloning human beings, it has been suggested that there might be exceptional cases in which cloning humans would be ethically permissible. One type of supposed exceptional case involves infertile couples who want to have children by cloning. This paper explores whether cloning would be ethically permissible in infertility cases and the separate question of whether we should have a policy allowing cloning in such cases. One caveat should be stated at the beginning, (...) however. After the cloning of a sheep in Scotland, scientists pointed out that using the same technique to clone humans would, at present, involve substantial risks of producing children with birth defects. This concern over safety gives compelling support to the view that it would be wrong to attempt human cloning now. Thus, we do not reach the debate about exceptional cases unless the issue of safety can be set aside. I ask the reader to consider the possibility that in the future humans could be cloned without a significantly elevated risk of birth defects from the cloning process itself. The remainder of this paper assumes, for sake of argument, that cloning technology has advanced to that point. Given this assumption, would cloning in the infertility cases be ethically permissible, and should it be legally permitted? (shrink)

The "space" of Lascar strong types, on some sort and relative to a given complete theory T, is in general not a compact Hausdorff topological space. We have at least three aims in this paper. The first is to show that spaces of Lascar strong types, as well as other related spaces and objects such as the Lascar group Gal L of T, have well-defined Borel cardinalities. The second is to compute the Borel cardinalities of the known examples (...) as well as of some new examples that we give. The third is to explore notions of definable map, embedding, and isomorphism, between these and related quotient objects. We also make some conjectures, the main one being roughly "smooth if and only if trivial". The possibility of a descriptive set-theoretic account of the complexity of spaces of Lascar strong types was touched on in the paper [E. Casanovas, D. Lascar, A. Pillay and M. Ziegler, Galois groups of first order theories, J. Math. Logic1 305–319], where the first example of a "non-G-compact theory" was given. The motivation for writing this paper is partly the discovery of new examples via definable groups, in [A. Conversano and A. Pillay, Connected components of definable groups and o-minimality I, Adv. Math.231 605–623; Connected components of definable groups and o-minimality II, to appear in Ann. Pure Appl. Logic] and the generalizations in [J. Gismatullin and K. Krupiński, On model-theoretic connected components in some group extensions, preprint, arXiv:1201.5221v1]. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:BOOK REVIEWS 273 Verene, Donald Phillip. Vico's Science of Imagination. Ithaca, New York: Cornell University Press, 1981, Pp. 227. $19.5o. In Chapter 1 (Introduction: Vico's Originality), Verene announces two principal concerns, a two-fold approach, and the predominant contention of his study.. 1. Principal concerns: "to consider the philosophical truth of Vico's ideas themselves, rather than to examine their historical character" (p. 19); to consider "the importance of Vico's conception (...) of barbarism for understanding present society" (p. 28). 2. Two-fold approach: "to interpret the central theses of Vico's thought" from the inside in the spirit of the whole and, at the same time, "to develop the problems of Vico's philosophy themselves" (pp. 19--21 ). 3. Predominant contention: "that Vico's ideas constitute a philosophy of recollective universals which generates philosophical understanding fronl the image, not the rational category. This approach regards imagination as a method of pfiilosophical thought" (p. 19) and the imaginative universal as "a key to his conception of knowledge" (p. 67). Vico's philosophy is depicted and characterized by Verene as fi)llows. Beginning with the imagination (fantasia) as an original and independent power of mind, Vico builds his philosophy on the image, the imaginative universal, thereby creating a position outside Western philosophy as traditionally understood. His New Science is a process of recollective fantasia, a kind of memory, and the system built constitutes a system of memory for all of human reality. By means of his concept of memory, Vico works his way back to the world of original thought, the mythicopoeticfantasia of the first men. His discovery of the imaginative universal as their way of thinking and their kind of knowledge establishes a new genetic origin for philosophical thought. Recollective fantasia constitutes the subject-matter and form of Vico's science itself', i.e., the term designates a type of nlemory through which the New Science is acconlplished as well as the type of thought from which it must be understood. "The New Science is a metaphysical fable, h creates a vera narratio of the recollectire imagination. The storia ideale eterna is an ideal trnth, but not an a priori or fictional one. As the master image of the recollective mind, it precisely contains all of the human event. Metaphysical truth, achieved through the exercise of.[antasia.., is generated out of the mind itself.., as images that actually contain the providential structure of reality" (p. 125). Vico's per|ornlative science "is man's true production of a knowledge of" his own nature" (p. 133). "The proof of the science is found through the reader making it for himself" (p. 156). What is the "recollective imaginative universal"? (a term coined by Verene) as distinguished from the universale fantastico? Vico identifies the latter quite simply. Poetic imagination, he tells us, was active in the first men who, "not being able to form intelligible class concepts of things, had a natural need to create poetic characters ; that is, imaginative class concepts or universals, to which, as to certain models or ideal portraits, to reduce all the particular species that resembled them." (The New Science of Giambattista Vico, trans. Thomas Goddard Bergin and Max Harold Fisch. Cornell University Press, 1968; orig. pub. 1948, w ) Thus in the theological age, 274 HISTORY OF PHILOSOPHY "Jove was born naturally in poetry as a divine character or imaginative universal, to which everything having to do with the auspices was referred by all the ancient gentile nations, which must therefore all have been poetic by nature" (9 381). In the age of heroes, Achilles embodies the idea of valor common to all strong men and Ulysses the idea of prudence common to all wise men (9 403). The myths, fables, and allegories brought to birth by poetic imagination were true stories for their makers. Imaginative universals or genera, "as the human mind later learned to abstract forms and properties from subjects, passed over into intelligible genera, which prepared the way for philosophers.... " (9 934)- Abstracting, categorizing, and predicating on the basis of properties in common, the philosophers in their intelligible class concepts no hmger think in the same manner as the first men did... (shrink)

From the perspective of investigators conducting research involving pregnant women and fetuses, a woman's decision about whether to have an abortion can sometimes be relevant to the suitability of the woman and fetus as research subjects. However, prominent ethicists disagree over whether it is permissible for a woman's decision about abortion to be an inclusion or exclusion criterion for participation in research. A widely held view is that fetuses to be aborted and fetuses to be carried to term should be (...) treated equally as research subjects. Some hold that this principle implies that a woman's decision about whether to have an abortion should not be an inclusion or exclusion criterion. This paper identifies types of research in which investigators might want to have inclusion or exclusion criteria based on decisions about abortion. It examines the arguments for and against having the woman's decision about abortion included in such criteria. It is argued that there are types of research in which such criteria are ethically permissible. (shrink)

This paper argues that for Nietzsche it is only when the strong type decays on its own terms that it is possible for a weak type to come into dominance by inverting the values of the strong. It sets right a latent inconsistency in Deleuze’s work, Nietzsche and Philosophy , which traces back the origin of decadence to the subterranean struggle between reactive forces. I show that Deleuze’s reading runs contrary to his own contention that for (...) Nietzsche the negative is a result of activity. I argue that the decadence of the strong is a consequence of its very creative activity and abundant health. Relying on Nietzsche’s later works, I isolate and analyze four typical traits of the strong type which not only determine this type as what it is but also make it vulnerable to decadence. (shrink)

An objection often is raised against the use of reproductive technology to create "nontraditional families," as in ovum donation for postmenopausal women or postmortem artificial insemination. The objection states that conceiving children in such circumstances is harmful to them because of adverse features of these nontraditional families. A similar objection is raised when parents, through negligence or willful disregard of risks, create children with serious genetic diseases or other developmental handicaps. It is claimed that such reproduction harms the children who (...) are created. In reply to this Harm to the Child Argument, it has been pointed out that the procreative acts that supposedly harm the child are the very acts that create the child. This reply has been developed into an argument that, in most of the types of cases under consideration, creating the child does not harm her. This reply, the No Harm Argument, has been stated in three main ways, and it is one of the most misunderstood arguments in bioethics. This paper examines the main rebuttals that have been made to the No Harm Argument and argues that none of them is successful. (shrink)

The strong normalization theorem is uniformly proved for typed λ-calculi for a wide range of substructural logics with or without strong negation.

The following strong form of density of definable types is introduced for theoriesTadmitting a fibered dimension functiond: given a modelMofTand a definable setX⊆Mn, there is a definable typepinX, definable over a code forXand of the samed-dimension asX. Both o-minimal theories and the theory of closed ordered differential fields are shown to have this property. As an application, we derive a new proof of elimination of imaginaries for CODF.

The aim of this paper is to introduce an alternative to Łukasiewicz’s 4-valued modal logic Ł. As it is known, Ł is afflicted by “Łukasiewicz type paradoxes”. The logic we define, PŁ4, is a strong paraconsistent and paracomplete 4-valued modal logic free from this type of paradoxes. PŁ4 is determined by the degree of truth-preserving consequence relation defined on the ordered set of values of a modification of the matrix MŁ characteristic for the logic Ł. On the (...) other hand, PŁ4 is a rich logic in which a number of connectives can be defined. It also has a simple bivalent semantics of the Belnap–Dunn type. (shrink)

The notion of a strongly determined type over A extending p is introduced, where p .S. A strongly determined extension of p over A assigns, for any model M )- A, a type q S extending p such that, if realises q, then any elementary partial map M → M which fixes acleq pointwise is elementary over . This gives a crude notion of independence which arises very frequently. Examples are provided of many different kinds of theories with (...) strongly determined types, and some without. We investigate a notion of multiplicity for strongly determined types with applications to ‘involved’ finite simple groups, and an analogue of the Finite Equivalence Relation Theorem. Lifting of strongly determined types to covers of a structure is discussed, and an application to finite covers is given. (shrink)

In this paper a model for barrecursion is presented. It has as a novelty that it contains discontinuous functionals. The model is based on a concept called strong majorizability. This concept is a modification of Howard's majorizability notion; see [T, p. 456].

Tait's proof of strong normalization for the simply typed λ-calculus is interpreted in a general model theoretical framework by means of the specification of a certain theory T and a certain model /oU of T. The argumentation is partly reduced to formal predicate logic by the application of certain derivability properties of T. The resulting version of Tait's proof is, within the same framework, systematically generalized to the Calculus of Constructions and other advanced type systems. The generalization proceeds (...) along the formal level in the sense that T is modified first and that the new theory partly dictates the subsequent transformation of /oU, which is carried out in stages. The uniform and standardized character of the argumentation contributes to its perspicuity. (shrink)

A simple proof is given of the property that the set of strongly normalizing lambda terms coincides with the set of lambda terms typable in certain intersection type assignment systems.

The storage operators were introduced by J.L. Krivine ([6]); they are closed λ-terms which, for some fixed data type (the integers for example), allow to simulate “call by value” while using “call by name”. J.L. Krivine showed that such operators can be typed, in the type system, using Gödel's translation from classical to intuitionistic logic ([8]).This paper studies the existence of storage operators which give a normal form as result (strong storage operators) for recursive and iterative representation (...) of data in λ-calculus. We obtain the following result:We can find typed strong storage operators for the recursive representations of data type, but that is not the case for the iterative representations of an infinite data type.We give the proof of this result in the case of integers. (shrink)

Transhumance is a form of extensive livestock production that involves seasonal movements among ecological zones or landscape types. Rangeland-based transhumance constitutes an important social and economic relationship to nature in many regions of the world, including across the Western US. However, social and ecological drivers of change are reshaping transhumant practices, and managers must adapt to increased demands for public rangeland use. Specifically, concerns for wildlife conservation have led to reduced access to seasonal public lands grazing for western US livestock (...) producers. To understand how managers adapt to loss of grazing areas (called “seasonal ranges”) we create agroecological calendars from manager records spanning 35 years (1986–2021) at the US Sheep Experiment Station in Idaho and Montana, US. The calendars illustrate how a loss of winter and summer ranges after 2013 coincided with shifts in the operation’s adaptive strategies, leading to more grazing of fall crop residue and purchased winter feed, and reducing flexibility to move livestock to cope with variable forage conditions. These changes shifted the job duties and experiences of farm workers and managers, and raised several new questions related to sheep production and vegetation management outcomes that merit future research. Transhumant system transformation has implications for human relationships with nature, rural communities, sheep genetics, production, and vegetation communities. For livestock operations that rely on government-managed lands to sustain transhumant traditions, innovative forms of collaboration and social adaptation that help secure access to seasonal ranges will be as important as technological innovations to address biodiversity conservation, climate change adaptation, and food system sustainability issues that are reshaping access to grazing lands. (shrink)

This paper presents the first purely algebraic characterization of classes of partial algebras definable by a set of strong equations. This result was posible due to new tools such as invariant congruences, i.e. a generalization of the notion of a fully invariant congruence, and extension of algebras, specific for strong equations.

We provide a new and elementary proof of strong normalization for the lambda calculus of intersection types. It uses no strong method, like for instance Tait-Girard reducibility predicates, but just simple induction on type complexity and derivation length and thus it is obviously formalizable within first order arithmetic. To obtain this result, we introduce a new system for intersection types whose rules are directly inspired by the reduction relation. Finally, we show that not only the set of (...) strongly normalizing terms of pure lambda calculus can be characterized in this system, but also that a straightforward modification of its rules allows to characterize the set of weakly normalizing terms. (shrink)

This paper defines reduction on derivations (cut-elimination) in the Strict Intersection Type Assignment System of an earlier paper and shows a strong normalization result for this reduction. Using this result, new proofs are given for the approximation theorem and the characterization of normalizability of terms using intersection types.

We study Lascar strong types and Galois types and especially their relation to notions of type which have finite character. We define a notion of a strong type with finite character, the so-called Lascar type. We show that this notion is stronger than Galois type over countable sets in simple and superstable finitary AECs. Furthermore, we give an example where the Galois type itself does not have finite character in such a class.

ArgumentIn the theory-dominated view of scientific experimentation, all relations of theory and experiment are taken on a par; namely, that experiments are performed solely to ascertain the conclusions of scientific theories. As a result, different aspects of experimentation and of the relations of theory to experiment remain undifferentiated. This in turn fosters a notion of theory-ladenness of experimentation (TLE) that is toocoarse-grainedto accurately describe the relations of theory and experiment in scientific practice. By contrast, in this article, I suggest that (...) TLE should be understood as anumbrella conceptthat has different senses. To this end, I introduce a three-fold distinction among the theories of high-energy particle physics (HEP) as background theories, model theories, and phenomenological models. Drawing on this categorization, I contrast two types of experimentation, namely, “theory-driven” and “exploratory” experiments, and I distinguish between the “weak” and “strong” senses of TLE in the context of scattering experiments from the history of HEP. This distinction enables identifying the exploratory character of the deep-inelastic electron-proton scattering experiments – performed at the Stanford Linear Accelerator Center (SLAC) between the years 1967 and 1973 – thereby shedding light on a crucial phase of the history of HEP, namely, the discovery of “scaling,” which was the decisive step towards the construction of quantum chromo-dynamics as a gauge theory of strong interactions. (shrink)

The logic BN4 was defined by R.T. Brady as a four-valued extension of Routley and Meyer’s basic logic B. The system EF4 is defined as a companion to BN4 to represent the four-valued system of implication. The system Ł was defined by J. Łukasiewicz and it is a four-valued modal logic that validates what is known as strong Łukasiewicz-type modal paradoxes. The systems EF4-M and EF4-Ł are defined as alternatives to Ł without modal paradoxes. This paper aims to (...) define a Belnap-Dunn semantics for EF4, EF4-M and EF4-Ł. It is shown that EF4, EF4-M and EF4-Ł are strongly sound and complete w.r.t. their respective semantics and that EF4-M and EF4-Ł are free from strong Łukasiewicz-type modal paradoxes. (shrink)

We show that several logics of common belief and common knowledge are not only complete, but also strongly complete, hence compact. These logics involve a weakened monotonicity axiom, and no other restriction on individual belief. The semantics is of the ordinary fixed-point type.

This paper proposes that both weak and strong NPIs in English are sensitive to the downward entailingness of their licensers. It is also proposed, however, that these two types of NPIs pay attention to different aspects of the meaning of their environment. As observed by von Fintel and Chierchia, weak NPIs do not attend to the scalar implicatures of presuppositions of their licensers. Strong NPIs see both the truth-conditional and non-truth-conditional (scalar implications, presuppositions) meaning of their licensers. This (...) theory accounts for the puzzling inability, noted by Rullmann and Gajewski, of Strawson anti-additive operators to license strong NPIs, as well as for the effects of Zwarts’s hierarchy of negative strength. Additional issues concerning comparative quantifiers, few, and proportional quantifiers are addressed. (shrink)

In this paper we propose an extension of Defeasible Logic to represent and compute different concepts of defeasible permission. In particular, we discuss some types of explicit permissive norms that work as exceptions to opposite obligations or encode permissive rights. Moreover, we show how strong permissions can be represented both with, and without introducing a new consequence relation for inferring conclusions from explicit permissive norms. Finally, we illustrate how a preference operator applicable to contrary-to-duty obligations can be combined with (...) a new operator representing ordered sequences of strong permissions. The logical system is studied from a computational standpoint and is shown to have linear computational complexity. (shrink)

Let MK3 I and MK3 II be Kleene's strong 3-valued matrix with only one and two designated values, respectively. Next, let MK3 G be defined exactly as MK3 I, except th...

We show that in the [Formula: see text] extension of a certain Chang-type model of determinacy, if [Formula: see text], then the restriction of the club filter on [Formula: see text] Cof[Formula: see text] to HOD is an ultrafilter in HOD. This answers Question 4.11 of [O. Ben-Neria and Y. Hayut, On [Formula: see text]-strongly measurable cardinals, Forum Math. Sigma 11 (2023) e19].

Neil Tennant’s core logic is a type of bilateralist natural deduction system based on proofs and refutations. We present a proof system for propositional core logic, explain its connections to bilateralism, and explore the possibility of using it as a type theory, in the same kind of way intuitionistic logic is often used as a type theory. Our proof system is not Tennant’s own, but it is very closely related, and determines the same consequence relation. The difference, (...) however, matters for our purposes, and we discuss this. We then turn to the question of strong normalization, showing that although Tennant’s proof system for core logic is not strongly normalizing, our modified system is. (shrink)

Marušić & Schwenkler (Analytic Philosophy, 59, 309) offer a simple and elegant defense of strong cognitivism about intention: the view that an intention to φ is a form of belief that one will φ. I show that their defense fails: however simple and elegant, it fails to account for various aspects about intention and its expression, and faces distinctive challenges of its own, including a dilemma and counterexample. These also undermine Marušić & Schwenkler's claim to a best-explanation type (...) of account and recommend alternatives to strong cognitivism altogether. (shrink)

Social anxiety and stress type can influence strong conformity among adolescents; however, the interaction between them is not clear. In this study, 152 adolescents were recruited and assigned one of two conditions: an interaction and a judgment condition. In the interaction condition, adolescents with high social anxiety (HSA) were less likely to conform when completing a modified Asch task, compared to adolescents who had low social anxiety. In the judgment condition, adolescents with HSA were more likely to conform (...) to the opinions from the unanimous majority. The results suggest that adolescents with HSA may show different styles of strong conformity with the change of stress type. We believe that socially anxious adolescents avoid potential social situations with weaker conformity, while avoiding negative evaluations from others with stronger conformity. These findings contribute to a better understanding of the social dysfunctions among adolescents with HSA and provide a new direction for clinical interventions. (shrink)

The meaning of sustainability is the subject of intense debate among environmental and resource economists. Perhaps no other issue separates more clearly the traditional economic view from the views of most natural scientists. The debate currently focuses on the substitutability between the economy and the environment or between “natural capital” and “manufactured capital”—a debate captured in terms of weak versus strong sustainability. In this article, we examine the various interpretations of these concepts. We conclude that natural science and economic (...) perspectives on sustainability are inconsistent. The market-based Hartwick-Solow “weak sustainability” approach is far removed from both the ecosystem-based “Holling sustainability” and the “strong sustainability” approach of Daly and others. Each of these sustainability criteria implies a specific valuation approach, and thus an ethical position, to support monetary indicators of sustainability such as a green or sustainable Gross Domestic Product (GDP). The conflict between “weak sustainability” and “strong sustainability” is more evident in the context of centralized than decentralized decision making. In particular, firms selling “services” instead of material goods and regarding the latter as “capital” leads to decisions more or less consistent with either type of sustainability. Finally, we discuss the implications of global sustainability for such open systems as regions and countries. Open systems have not been dealt with systematically for any of the sustainability criteria. (shrink)

Boycotts are among the most frequent forms of consumer expression against unethical or egregious acts by firms. Most current research explains consumers’ decisions to participate in a boycott using a universal cost-benefit model that mixes instrumental and expressive motives. To date, no conceptual framework accounts for the distinct behavioral motives for boycotting though. This article focuses on motivational heterogeneity among consumers. By distinguishing two stable behavioral models—a self-regarding type and a strongly reciprocal type—we introduce the notion of (...) class='Hi'>strong reciprocity to the boycott literature. We argue that the presence of strongly reciprocal consumers can enhance boycott success. First, in interactions with the target firm, strongly reciprocal consumers perceive higher levels of egregiousness and are more willing to engage in boycotting behavior, even in unfavorable strategic conditions, which provides a stable basis for boycotting. Second, in interactions with self-regarding consumers, strongly reciprocal consumers are willing to sanction those others, according to whether they participate in the boycott, which increases overall participation in and the likelihood of success of a consumer boycott. These findings have implications for further research, as well as for firms, nongovernmental organizations, and boycotters. (shrink)

We prove the strong normalization of full classical natural deduction by using a translation into the simply typed λμ-calculus. We also extend Mendler’s result on recursive equations to this system.

The method of strong inference, wherein multiple hypotheses are constructed and a crucial experiment is carried out, is said to have special status in science because it guarantees falsifying results. However, the proposition that strong inference is in any way superior to the method of constructing and testing a single hypothesis is contradicted both by close rational analysis and by the empirical evidence. An experiment is reviewed in which subjects who conduct strong tests are much less likely (...) to discover or approximate the truth than subjects who conduct simple tests of a false hypothesis. It is concluded that a potential to falsify is necessary for a test to have corroborative value; however, arguments as to the general superiority of one type of potentially falsifying test over another have no logical basis. Any claim as to a general superiority of strong tests over simple tests would require access to information about the probability of each strategy to produce various relationships between the truth and whatever explanations are most accessible, and such information is not knowable, even in principle. (shrink)

In the domain of ontology design as well as in Knowledge Representation, modeling universals is a challenging problem.Most approaches that have addressed this problem rely on Description Logics (DLs) but many difficulties remain, due to under-constrained representation which reduces the inferences that can be drawn and further causes problems in expressiveness. In mathematical logic and program checking, type theories have proved to be appealing but, so far they have not been applied in the formalization of ontologies. To bridge this (...) gap, we present in this paper a theory for representing ontologies in a dependently typed framework which relies on strong formal foundations including both a constructive logic and a functional type system. The language of this theory defines in a precise way what ontological primitives such as classes, relations, properties, etc., and thereof roles, are. The first part of the paper details how these primitives are defined and used within the theory. In a second part, we focus on the formalization of the role primitive. A review of significant role properties leads to the specification of a role profile and most of the remaining work details through numerous examples, how the proposed theory is able to fully satisfy this profile. It is demonstrated that dependent types can model several non-trivial aspects of roles including a formal solution for generalization hierarchies, identity criteria for roles and other contributions. A discussion is given on how the theory is able to cope with many of the constraints inherent in a good role representation. (shrink)

In the theory-dominated view of scientific experimentation, all relations of theory and experiment are taken on a par; namely, that experiments are performed solely to ascertain the conclusions of scientific theories. As a result, different aspects of experimentation and of the relation of theory to experiment remain undifferentiated. This in turn fosters a notion of theory-ladenness of experimentation that is too coarse-grained to accurately describe the relations of theory and experiment in scientific practice. By contrast, in this article, I suggest (...) that TLE should be understood as an umbrella concept that has different senses. To this end, I introduce a three-fold distinction among the theories of high-energy particle physics as background theories, model theories and phenomenological models. Drawing on this categorization, I contrast two types of experimentation, namely, “theory-driven” and “exploratory” experiments, and I distinguish between the “weak” and “strong” senses of TLE in the context of scattering experiments from the history of HEP. This distinction enables to identify the exploratory character of the deep-inelastic electron-proton scattering experiments—performed at the Stanford Linear Accelerator Center between the years 1967 and 1973—thereby shedding light on a crucial phase of the history of HEP, namely, the discovery of “scaling”, which was the decisive step towards the construction of quantum chromo-dynamics as a gauge theory of strong interactions. (shrink)

In this paper we study the relativized Lascar Galois group of a strong type. The group is a quasi-compact connected topological group, and if in addition the underlying theory T is G-compact, then the group is compact. We apply compact group theory to obtain model theoretic results in this note. -/- For example, we use the divisibility of the Lascar group of a strong type to show that, in a simple theory, such types have a certain (...) model theoretic property that we call divisible amalgamation. -/- The main result of this paper is that if c is a finite tuple algebraic over a tuple a, the Lascar group of stp(ac) is abelian, and the underlying theory is G-compact, then the Lascar groups of stp(ac) and of stp(a) are isomorphic. To show this, we prove a purely compact group-theoretic result that any compact connected abelian group is isomorphic to its quotient by every finite subgroup. -/- Several (counter)examples arising in connection with the theoretical development of this note are presented as well. For example, we show that, in the main result above, neither the assumption that the Lascar group of stp(ac) is abelian, nor the assumption of c being finite can be removed. (shrink)

We give the first systematic study of strong isomorphism reductions, a notion of reduction more appropriate than polynomial time reduction when, for example, comparing the computational complexity of the isomorphim problem for different classes of structures. We show that the partial ordering of its degrees is quite rich. We analyze its relationship to a further type of reduction between classes of structures based on purely comparing for every n the number of nonisomorphic structures of cardinality at most n (...) in both classes. Furthermore, in a more general setting we address the question of the existence of a maximal element in the partial ordering of the degrees. (shrink)

I In this paper, we investigate the nature of empirical hypotheses used in scientific reasoning and the act of formulating hypotheses. This is achieved through a novel logical framework in which we provide specific semantics for two types of hypotheses: a strong and a weak sense of hypothesis, each characterized by different logical structures. This framework enables us to better characterize certain aspects of hypothetical reasoning in scientific practice, especially when we attempt to rationally deny the content of an (...) empirical hypothesis. (shrink)

In the context of state educational institutions, young white males are owed a duty to respect their interest or desert tokens. Not all white males have waived this duty since many white males have not performed the relevant types of culpable wrongdoing. Merely having benefitted from an unjust injury act or being a member of a community that owe a debt of compensation to racial minorities and women are not sufficient grounds to override the duty owed to the white male. (...) Since the three most plausible attempts to provide a compensatory justice justification for strong affirmative action programs at state educational institutions fail, I conclude that the following is false. (1) Other things being equal, a state educational institution may choose to hire a less qualified candidate over a more qualified candidate because the weight given to the race or gender of the less qualified candidate relates to the elimination of a debt of compensatory justice. Hence, unless strong affirmative action programs at state educational institutions can be justified by reference to some other value, such as the value of diversity, the state ought to eliminate such programs. (shrink)

An (n, k)-ary quantifier is a generalized logical connective, binding k variables and connecting n formulas. Canonical systems with (n, k)-ary quantifiers form a natural class of Gentzen-type systems which in addition to the standard axioms and structural rules have only logical rules in which exactly one occurrence of a quantifier is introduced. The semantics for these systems is provided using two-valued non-deterministic matrices, a generalization of the classical matrix. In this paper we use a constructive syntactic criterion of (...) coherence to characterize strong cutelimination in such systems. We show that the following properties of a canonical system G with arbitrary (n, k)-ary quantifiers are equivalent: (i) G is coherent, (ii) G admits strong cut-elimination, and (iii) G has a strongly characteristic two-valued generalized non-deterministic matrix. In addition, we define simple calculi, an important subclass of canonical calculi, for which coherence is equivalent to the weaker, standard cut-elimination property. (shrink)