An ω-categorical supersimple group is finite-by-abelian-by-finite, and has finite SU-rank. Every definable subgroup is commensurable with an acl( $\emptyset$ )-definable subgroup. Every finitely based regular type in a CM-trivial ω-categorical simple theory is non-orthogonal to a type of SU-rank 1. In particular, a supersimple ω-categorical CM-trivial theory has finite SU-rank.

An $\omega$-categorical supersimple group is finite-by-abelian-by-finite, and has finite SU-rank. Every definable subgroup is commensurable with an acl-definable subgroup. Every finitely based regular type in a CM-trivial $\omega$-categorical simple theory is non-orthogonal to a type of SU-rank 1. In particular, a supersimple $\omega$-categorical CM-trivial theory has finite SU-rank.

Assume T is unidimensional, 1-based and every minimal type in T is locally finite. If H is an Λ -definable irreducible group, we find an irreducible supergroup G of H in acleq such that any connected subgroup of Gn, n < ω, is the connected component of a subgroup linearly defined over the ring End*. In some cases we can take G = H.

It is shown that for every Turing degree d there is an ω-categorical group G such that the isomorphism type of G is of degree d. We also find an ω-categorical group G such that the isomorphism type of G has no degree.

We prove that each ω-categorical, generically stable group is solvable-by-finite.

We investigate effective categoricity of computable Abelian p-groups . We prove that all computably categorical Abelian p-groups are relatively computably categorical, that is, have computably enumerable Scott families of existential formulas. We investigate which computable Abelian p-groups are categorical and relatively categorical.

It is shown that no infinite group is interpretable in any structure which is homogeneous in a finite relational language. Related questions are discussed for other ω-categorical structures.

We prove that every ω-categorical, generically stable group is nilpotent-by-finite and that every ω-categorical, generically stable ring is nilpotent-by-finite.

We consider structures A consisting of an abelian group with a subgroup AP distinguished by a 1-ary relation symbol P, and complete theories T of such structures. Such a theory T is -categorical if T has models A of cardinality λ with AP=κ, and given any two such models A,B with AP=BP, there is an isomorphism from A to B which is the identity on AP. We classify all complete theories of such structures A in terms of the (...) cardinal pairs in which they are categorical. We classify algebraically the A of finite order λ with AP of order κ which are -categorical. (shrink)

Humans appear to be possible candidates for group selection because they are often said to live in bands, clans, and tribes. These terms, however, are only names for conceptual categories of people. They do not designate enduring bounded gatherings of people that might be “vehicles of selection.” Hence, group selection has probably not been a major force in human evolution.

In this paper we prove that the category of abelianl-groups is equivalent to the category of perfect MV-algebras. Furthermore, we give a finite equational axiomatization of the variety generated by perfect MV-algebras.

Using new techniques for controlling the categoricity spectrum of a structure, we construct a structure with degree of categoricity but infinite spectral dimension, answering a question of Bazhenov, Kalimullin and Yamaleev. Using the same techniques, we construct a computably categorical structure of non-computable Scott rank.

We extend Morley's Theorem to show that if a theory is κ-p-categorical for some uncountable cardinal κ, it is uncountably categorical. We then discuss ω-p-categoricity and provide examples to show that similar extensions for the Baldwin-Lachlan and Lachlan Theorems are not possible.

A classic result in the foundations of Yang-Mills theory, due to J. W. Barrett ["Holonomy and Path Structures in General Relativity and Yang-Mills Theory." Int. J. Th. Phys. 30, ], establishes that given a "generalized" holonomy map from the space of piece-wise smooth, closed curves based at some point of a manifold to a Lie group, there exists a principal bundle with that group as structure group and a principal connection on that bundle such that the holonomy (...) map corresponds to the holonomies of that connection. Barrett also provided one sense in which this "recovery theorem" yields a unique bundle, up to isomorphism. Here we show that something stronger is true: with an appropriate definition of isomorphism between generalized holonomy maps, there is an equivalence of categories between the category whose objects are generalized holonomy maps on a smooth, connected manifold and whose arrows are holonomy isomorphisms, and the category whose objects are principal connections on principal bundles over a smooth, connected manifold. This result clarifies, and somewhat improves upon, the sense of "unique recovery" in Barrett's theorems; it also makes precise a sense in which there is no loss of structure involved in moving from a principal bundle formulation of Yang-Mills theory to a holonomy, or "loop", formulation. (shrink)

An explicit categorical equivalence is defined between a proper subvariety of the class of \-algebras, as defined by Di Nola and Dvurečenskij, to be called \-algebras, and the category of semi-low \-rings. This categorical representation is done using the prime spectrum of the \-algebras, through the equivalence between \-algebras and \-groups established by Mundici, from the perspective of the Dubuc–Poveda approach, that extends the construction defined by Chang on chains. As a particular case, semi-low \-rings associated to Boolean (...) algebras are characterized. (shrink)

An explicit categorical equivalence is defined between a proper subvariety of the class of \-algebras, as defined by Di Nola and Dvurečenskij, to be called \-algebras, and the category of semi-low \-rings. This categorical representation is done using the prime spectrum of the \-algebras, through the equivalence between \-algebras and \-groups established by Mundici, from the perspective of the Dubuc–Poveda approach, that extends the construction defined by Chang on chains. As a particular case, semi-low \-rings associated to Boolean (...) algebras are characterized. (shrink)

David Gauthier suggested that all genuine moral problems are Prisoners Dilemmas (PDs), and that the morally and rationally required solution to a PD is to co-operate. I say there are four other forms of moral problem, each a different way of agents failing to be in PDs because of the agents’ preferences. This occurs when agents have preferences that are malevolent, self-enslaving, stingy, or bullying. I then analyze preferences as reasons for action, claiming that this means they must not target (...) the impossible, they must be able to be acted on in the circumstances, their targets must be attainable, and having the preferences must make their targets more likely. For groups of agents to have a distribution of preferences, their preferences must jointly have those four features, this imposing a kind of universalizability requirement on possible preferences. I then claim that, if all agents began with preferences satisfying these requirements, their preferences would not be of the morally problematic sort (on pain, variously, of circularity or contradiction in the specification of their targets). Instead, they would be either morally innocent preferences, or ones which put the agents in PDs. And it would then be instrumentally rational for the agents to prefer mutual co-operation. Thus if all agents initially had rationally permissible preferences and made rational choices of actions and preferences thereafter, they would never acquire immoral preferences, and so never be rationally moved to immoral actions. Further, the states of affairs such agents would be moved to bring about would be compatible with what Rawls’ agents would chose behind a veil of ignorance. Morality therefore reduces to rationality; necessarily, the actions categorically required by morality are also categorically required by rationality. (shrink)

In this paper we provide a categorical equivalence for the category \ of product algebras, with morphisms the homomorphisms. The equivalence is shown with respect to a category whose objects are triplets consisting of a Boolean algebra B, a cancellative hoop C and a map \ from B × C into C satisfying suitable properties. To every product algebra P, the equivalence associates the triplet consisting of the maximum boolean subalgebra B, the maximum cancellative subhoop C, of P, and (...) the restriction of the join operation to B × C. Although several equivalences are known for special subcategories of \ , up to our knowledge, this is the first equivalence theorem which involves the whole category of product algebras. The syntactic counterpart of this equivalence is a syntactic reduction of classical logic CL and of cancellative hoop logic CHL to product logic, and viceversa. (shrink)

We continue our study of finitary abstract elementary classes, defined in [7]. In this paper, we prove a categoricity transfer theorem for a case of simple finitary AECs. We introduce the concepts of weak κ-categoricity and f-primary models to the framework of א₀-stable simple finitary AECs with the extension property, whereby we gain the following theorem: Let (������, ≼ ������ ) be a simple finitary AEC, weakly categorical in some uncountable κ. Then (������, ≼ ������ ) is weakly (...) class='Hi'>categorical in each λ ≥ min { \group{ \{\kappa,\beth_{ \group{ (2^{ \aleph_{ 0 _} ^});^{ + ^} \group} _}\}; \group} . If the class (������, ≼ ������ ) is also LS(������)-tame, weak κ-categoricity is equivalent with κ-categoricity in the usual sense. We also discuss the relation between finitary AECs and some other non-elementary frameworks and give several examples. (shrink)

We study the computational complexity of deciding whether a given set of term equalities and inequalities has a solution in an ω-categorical algebra ????. There are ω-categorical groups where this pro...

We study the computational complexity of deciding whether a given set of term equalities and inequalities has a solution in an ω-categorical algebra ????. There are ω-categorical groups where this pro...

Our purpose in this note is to study countable ℵ0-categorical structures whose theories are tree-decomposable in the sense of Baldwin and Shelah. The permutation group corresponding to such a structure can be decomposed in a canonical manner into simpler permutation groups in the same class. As an application of the analysis we show that these structures are finitely homogeneous.

A commutative BCK-algebra with the relative cancellation property is a commutative BCK-algebra (X;*,0) which satisfies the condition: if a ≤ x, a ≤ y and x * a = y * a, then x = y. Such BCK-algebras form a variety, and the category of these BCK-algebras is categorically equivalent to the category of Abelian ℓ-groups whose objects are pairs (G, G 0), where G is an Abelian ℓ-group, G 0 is a subset of the positive cone generating G (...) + such that if u, v ∈ G 0, then 0 ∨ (u - v) ∈ G 0, and morphisms are ℓ-group homomorphisms h: (G, G 0) → (G′,G′0) with f(G 0) ⫅ G′0. Our methods in particular cases give known categorical equivalences of Cornish for conical BCK-algebras and of Mundici for bounded commutative BCK-algebras (= MV-algebras). (shrink)

The categorical imperative can be construed as a universalization test for moral permissibility. False negatives of the categorical imperative would be maxims failing this test, despite the permissibility of their actions; maxims like: ‘I’ll withdraw all my savings on April 15th’. Examples of purported false negatives familiar from the literature can be grouped into three general categories, and dispatched by applying category-specific methods for proper formulation of their maxims, or for proper testing. Methods for reformulating failing maxims, such (...) as the addition of appropriate conditional clauses, do not generate false-positive counterexamples in other instances. (shrink)

A first-order structure $\mathfrak {A}$ is called monadically stable iff every expansion of $\mathfrak {A}$ by unary predicates is stable. In this paper we give a classification of the class $\mathcal {M}$ of $\omega $ -categorical monadically stable structure in terms of their automorphism groups. We prove in turn that $\mathcal {M}$ is the smallest class of structures which contains the one-element pure set, is closed under isomorphisms, and is closed under taking finite disjoint unions, infinite copies, and finite (...) index first-order reducts. Using our classification we show that every structure in $\mathcal {M}$ is first-order interdefinable with a finitely bounded homogeneous structure. We also prove that every structure in $\mathcal {M}$ has finitely many reducts up to interdefinability, thereby confirming Thomas’ conjecture for the class $\mathcal {M}$. (shrink)

ABSTRACT Genetics research, like research in sociology and anthropology, creates risks for groups from which research subjects are drawn. This paper considers what sort of protection for groups from the risks of genetics research should be provided and by whom. The paper categorizes harms by distinguishing process‐related from outcome‐related harms and by distinguishing two kinds of group harms. It argues that calls for community engagement are justified with respect to some kinds of harms, but not with respect to others; (...) and it cautions that community engagement may itself be harmful. (shrink)

In a recent communication an uncountably categorical group has been constructed that has a non-locally-modular geometry and does not allow the interpretation of a field. We consider a system Δ of elementary axioms fulfilled by some special subgroups of the above group. We show that Δ is complete and stable, but not superstable. It is not even a R-group in the sense discussed by Wagner.

In recent work, the authors have established the group configuration theorem for simple theories, as well as some of its main applications from geometric stability theory, such as the binding group theorem, or in the $\omega$-categorical case, the characterization of the forking geometry of a finitely based non-trivial locally modular regular type as projective geometry over a finite field and the equivalence of pseudolinearity and local modularity. The proof necessitated an extension of the model-theoretic framework to include (...) almost hyperimaginaries, and the study of polygroups. (shrink)

We generalise the correspondence between $\aleph _0$ -categorical theories and their automorphism groups to arbitrary complete theories in classical logic, and to some theories in continuous logic.

We introduce Lascar strong types in excellent classes and prove that they coincide with the orbits of the group generated by automorphisms fixing a model. We define a new independence relation using Lascar strong types and show that it is well-behaved over models, as well as over finite sets. We then develop simplicity and show that, under simplicity, the independence relation satisfies all the properties of nonforking in a stable first order theory. Further, simplicity for an excellent class, as (...) well as the independence relation itself, is uniquely determined. Finally, we show that an excellent class is simple if and only if it has extensible U-rank . We deduce that any excellent class of finite U-rank is simple, and that any uncountably categorical excellent class has an expansion with countably many constants which is simple. (shrink)

Among the complete ℵ0-categorical theories with finite non-logical vocabularies, we distinguish three classes. The classification is obtained by looking at the number of bound variables needed to isolated complete types. In classI theories, all types are isolated by quantifier free formulas; in classII theories, there is a leastm, greater than zero, s.t. all types are isolated by formulas in no more thanm bound variables: and in classIII theories, for eachm there is a type which cannot be isolated inm or (...) fewer bound variables. ClassII theories are further subclassified according to whether or not they can be extended to classI theories by the addition of finitely many new predicates. Alternative characterizations are given in terms of quantifier elimination and homogeneous models. It is shown that for each primep, the theory of infinite Abelian groups all of whose elements are of orderp is classI when formulated in functional constants, and classIII when formulated in relational constants. (shrink)

Intersectional feminist scholars emphasize how overlapping systems of oppression structure gender inequality, but in focusing on the gendered, classed, and racialized bases of stratification, many often overlook disability as an important social category in determining economic outcomes. This is a significant omission given that disability severely limits opportunities and contributes to cumulative disadvantage. We draw from feminist disability and intersectional theories to account for how disability intersects with gender, race, and education to produce economic insecurity. The findings from our analyses (...) of 2015 American Community Survey data provide strong empirical support for hierarchies of disadvantage, where women and racial minority groups with disabilities and less education experience the highest poverty levels, report the lowest total income, and have a greater reliance on sources outside the labor market for economic security. By taking disability into account, our study demonstrates how these multiple characteristics lead to overlapping oppressions that become embedded and reproduced within the larger social structure. (shrink)

We study relationships between certain algebraic properties of groups and rings definable in a first order structure or *-closed in a compact G-space. As a consequence, we obtain a few structural results about ω-categorical rings as well as about small, nm-stable compact G-rings, and we also obtain surprising relationships between some conjectures concerning small profinite groups.

Our purpose in this note is to study countable $\aleph_0$-categorical structures whose theories are tree-decomposable in the sense of Baldwin and Shelah. The permutation group corresponding to such a structure can be decomposed in a canonical manner into simpler permutation groups in the same class. As an application of the analysis we show that these structures are finitely homogeneous.

N₀-stable N₀-categorical linked quaternionic mappings are studied and are shown to correspond (in some sense) to special groups which are N₀-stable. N₀-categorical, satisfy AP(3) and have finite 2-symbol length. They are also related to special groups whose isometry relation is a finite union of cosets, which are then considered on their own, as well as their links with pseudofinite, profinite and weakly normal special groups.

Music impacting on speech processing is vividly evidenced in most reports involving professional musicians, while the question of whether the facilitative effects of music are limited to experts or may extend to amateurs remains to be resolved. Previous research has suggested that analogous to language experience, musicianship also modulates lexical tone perception but the influence of amateur musical experience in adulthood is poorly understood. Furthermore, little is known about how acoustic information and phonological information of lexical tones are processed by (...) amateur musicians. This study aimed to provide neural evidence of cortical plasticity by examining categorical perception of lexical tones in Chinese adults with amateur musical experience relative to the non-musician counterparts. Fifteen adult Chinese amateur musicians and an equal number of non-musicians participated in an event-related potential (ERP) experiment. Their mismatch negativities (MMNs) to lexical tones from Mandarin Tone 2–Tone 4 continuum and non-speech tone analogs were measured. It was hypothesized that amateur musicians would exhibit different MMNs to their non-musician counterparts in processing two aspects of information in lexical tones. Results showed that the MMN mean amplitude evoked by within-category deviants was significantly larger for amateur musicians than non-musicians regardless of speech or non-speech condition. This implies the strengthened processing of acoustic information by adult amateur musicians without the need of focused attention, as the detection of subtle acoustic nuances of pitch was measurably improved. In addition, the MMN peak latency elicited by across-category deviants was significantly shorter than that by within-category deviants for both groups, indicative of the earlier processing of phonological information than acoustic information of lexical tones at the pre-attentive stage. The results mentioned above suggest that cortical plasticity can still be induced in adulthood, hence non-musicians should be defined more strictly than before. Besides, the current study enlarges the population demonstrating the beneficial effects of musical experience on perceptual and cognitive functions, namely, the effects of enhanced speech processing from music are not confined to a small group of experts but extend to a large population of amateurs. (shrink)

We reconstruct the group action in the group configuration theorem. We apply it to show that in an ω-categorical theory a finitely based pseudolinear regular type is locally modular, and the geometry associated to a finitely based locally modular regular type is projective geometry over a finite field.

We study classes of right-angled Coxeter groups with respect to the strong submodel relation of a parabolic subgroup. We show that the class of all right-angled Coxeter groups is not smooth and establish some general combinatorial criteria for such classes to be abstract elementary classes (AECs), for them to be finitary, and for them to be tame. We further prove two combinatorial conditions ensuring the strong rigidity of a right-angled Coxeter group of arbitrary rank. The combination of these results (...) translates into a machinery to build concrete examples of AECs satisfying given model-theoretic properties. We exhibit the power of our method by constructing three concrete examples of finitary classes. We show that the first and third classes are nonhomogeneous and that the last two are tame, uncountably categorical, and axiomatizable by a single Lω1,ω-sentence. We also observe that the isomorphism relation of any countable complete first-order theory is κ-Borel reducible (in the sense of generalized descriptive set theory) to the isomorphism relation of the theory of right-angled Coxeter groups whose Coxeter graph is an infinite random graph. (shrink)

In the context of continuous logic, this paper axiomatizes both the class \ of lattice-ordered groups isomorphic to C for X compact and the subclass \ of structures existentially closed in \; shows that the theory of \ is \-categorical and admits elimination of quantifiers; establishes a Nullstellensatz for \ and \; shows that \\in \mathcal {C}\) has a prime-model extension in \ just in case X is Boolean; and proves that in a sense relevant to continuous logic, positive (...) formulas admit in \ elimination of quantifiers to positive formulas. (shrink)

There exist two conjectures for constraint satisfaction problems of reducts of finitely bounded homogeneous structures: the first one states that tractability of the CSP of such a structure is, when the structure is a model-complete core, equivalent to its polymorphism clone satisfying a certain nontrivial linear identity modulo outer embeddings. The second conjecture, challenging the approach via model-complete cores by reflections, states that tractability is equivalent to the linear identities satisfied by its polymorphisms clone, together with the natural uniformity on (...) it, being nontrivial. We prove that the identities satisfied in the polymorphism clone of a structure allow for conclusions about the orbit growth of its automorphism group, and apply this to show that the two conjectures are equivalent. We contrast this with a counterexample showing that [Formula: see text]-categoricity alone is insufficient to imply the equivalence of the two conditions above in a model-complete core. Taking another approach, we then show how the Ramsey property of a homogeneous structure can be utilized for obtaining a similar equivalence under different conditions. We then prove that any polymorphism of sufficiently large arity which is totally symmetric modulo outer embeddings of a finitely bounded structure can be turned into a nontrivial system of linear identities, and obtain nontrivial linear identities for all tractable cases of reducts of the rational order, the random graph, and the random poset. Finally, we provide a new and short proof, in the language of monoids, of the theorem stating that every [Formula: see text]-categorical structure is homomorphically equivalent to a model-complete core. (shrink)

Triage situations and other occurrences in which rationing of medical care is necessary require careful distribution of medical equipment, services, or resources. However, the evolution of triage has failed to eliminate certain biases in the standards of care, particularly for groups already facing societal disenfranchisement and discrimination. This article explores the use of triage calculators and other systems of rationing care, their implicit biases, and how to avoid allowing those biases to influence care.

We establish, generalizing Di Nola and Lettieri’s categorical equivalence, a Morita-equivalence between the theory of lattice-ordered abelian groups and that of perfect MV-algebras. Further, after observing that the two theories are not bi-interpretable in the classical sense, we identify, by considering appropriate topos-theoretic invariants on their common classifying topos, three levels of bi-interpretability holding for particular classes of formulas: irreducible formulas, geometric sentences, and imaginaries. Lastly, by investigating the classifying topos of the theory of perfect MV-algebras, we obtain various (...) results on its syntax and semantics also in relation to the cartesian theory of the variety generated by Chang’s MV-algebra, including a concrete representation for the finitely presentable models of the latter theory as finite products of finitely presentable perfect MV-algebras. Among the results established on the way, we mention a Morita-equivalence between the theory of lattice-ordered abelian groups and that of cancellative lattice-ordered abelian monoids with bottom element. (shrink)