Let T be a complete, superstable theory with fewer than ${2^{\aleph_{0}}}$ countable models. Assuming that generic types of infinite, simple groups definable in T eq are sufficiently non-isolated we prove that ω ω is the strict upper bound for the Lascar rank of T.

We show that any simple group of Morley rank 5 is a bad group all of whose proper definable connected subgroups are nilpotent of rank at most 2. The main result is then used to catalog the nonsoluble connected groups of Morley rank 5.

The notion of ecological rationality implies that the accuracy of a decision strategy depends on features of the information environment in which it is tested. We demonstrate that the performance of a group may be strongly affected by the decision strategies used by its individual members and specify how this effect is moderated by environmental features. Specifically, in a set of simulation studies, we systematically compared four decision strategies used by the individual group members: two linear, compensatory decision (...) strategies and two simple, noncompensatory heuristics. Individual decisions were aggregated by using a majority rule. To assess the ecological rationality of the strategies, we varied (a) the distribution of cue validities, (b) the quantity, and (c) the quality of shared information. Group performance strongly depended on the distribution of cue validities. When validities were linearly distributed, groups using a compensatory strategy achieved the highest accuracy. Conversely, when cue validities followed a J-shaped distribution, groups using a simple lexicographic heuristic performed best. While these effects were robust across different quantities of shared information, the quality of shared information exerted stronger effects on group performance. Consequences for prescriptive theories on group decision making are discussed. (shrink)

In this paper we apply social epistemology to mathematical proofs and their role in mathematical knowledge. The most famous modern collaborative mathematical proof effort is the Classification of Finite Simple Groups. The history and sociology of this proof have been well-documented by Alma Steingart (2012), who highlights a number of surprising and unusual features of this collaborative endeavour that set it apart from smaller-scale pieces of mathematics. These features raise a number of interesting philosophical issues, but have received very (...) little attention. In this paper, we will consider the philosophical tensions that Steingart uncovers, and use them to argue that the best account of the epistemic status of the Classification Theorem will be essentially and ineliminably social. This forms part of the broader argument that in order to understand mathematical proofs, we must appreciate their social aspects. (shrink)

Simple Heuristics That Make Us Smart invites readers to embark on a new journey into a land of rationality that differs from the familiar territory of cognitive science and economics. Traditional views of rationality tend to see decision makers as possessing superhuman powers of reason, limitless knowledge, and all of eternity in which to ponder choices. To understand decisions in the real world, we need a different, more psychologically plausible notion of rationality, and this book provides it. It is (...) about fast and frugal heuristics--simple rules for making decisions when time is pressing and deep thought an unaffordable luxury. These heuristics can enable both living organisms and artificial systems to make smart choices, classifications, and predictions by employing bounded rationality. But when and how can such fast and frugal heuristics work? Can judgments based simply on one good reason be as accurate as those based on many reasons? Could less knowledge even lead to systematically better predictions than more knowledge? Simple Heuristics explores these questions, developing computational models of heuristics and testing them through experiments and analyses. It shows how fast and frugal heuristics can produce adaptive decisions in situations as varied as choosing a mate, dividing resources among offspring, predicting high school drop out rates, and playing the stock market. As an interdisciplinary work that is both useful and engaging, this book will appeal to a wide audience. It is ideal for researchers in cognitive psychology, evolutionary psychology, and cognitive science, as well as in economics and artificial intelligence. It will also inspire anyone interested in simply making good decisions. (shrink)

In his testamentary letter to Auguste Chevalier, Évariste Galois states that, in modern terminology, the smallest simple group has order 60. No proof of this statement survives in his papers, and it has been suggested that a proof would have been impossible using the methods available at the time. We argue that this assertion is unduly pessimistic. Moreover, one fragmentary document, dismissed as a triviality and misunderstood, looks suspiciously like cryptic notes related to this result. We give an (...) elementary proof of Galois’s statement, explain why it is likely that he would have been aware of the methods involved, and discuss the potential relevance of the fragment. (shrink)

We develop the theory of germs of generic functions in simple theories. Starting with an algebraic quadrangle (or other similar hypotheses), we obtain an "almost" generic group chunk, where the product is denned up to a bounded number of possible values. This is the first step towards the proof of the group configuration theorem for simple theories, which is completed in [3].

We study hyperdefinable groups, the most general kind of groups interpretable in a simple theory. After developing their basic theory, we prove the appropriate versions of Hrushovski's group quotient theorem and the Weil–Hrushovski group chunk theorem. We also study locally modular hyperdefinable groups and prove that they are bounded-by-Abelian-by-bounded. Finally, we analyze hyperdefinable groups in supersimple theories.

We talk about groups as doing something, we talk as if groups have agency. Is our talk legitimate? Are there group agents? Is there something like group agency? In this paper, I discuss two ontological frameworks concerning existence questions: the Quinean framework and the Thomasson-Carnap framework. I apply them to the problem of group agency. I review the Quinean-oriented literature debating the existence of group agents and its methodological background. I argue, via Thomasson’s easy approach to (...) ontology, that deflationism can simplify the debate surrounding group agents. Thus, I argue for a Thomasson-Carnap framework and show that it is better suited to answer the particular question whether there are group agents. More specifically, I argue for a non-reductive simple realist view on group agents, i.e. I argue for the truth of “There are group agents,” via analytic entailments, by truths about the actions and deeds of groups. (shrink)

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 generalize tools and results from first order stable theories to groups inside a simple stable strongly homogeneous model.

We continue the study of simple theories begun in [3] and [5]. We first find the right analogue of definability of types. We then develop the theory of generic types and stabilizers for groups definable in simple theories. The general ideology is that the role of formulas (or definability) in stable theories is replaced by partial types (or ∞-definability) in simple theories.

The binding group theorem for stable theories is partially extended to the simple context. Some results concerning internality are proved. We also introduce a ‘small’ normal subgroup G0+ of the automorphism group and show that if p is Q-internal then it has a finite exponent and G/G0+ is interpretable.

We show that any simple group of Morley rank 4 must be a bad group with no proper definable subgroups of rank larger than 1. We also give an application to groups acting on sets of Morley rank 2.

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.

In a simple theory with elimination of finitary hyperimaginaries if tp(a) is real and analysable over a definable set Q, then there exists a finite sequence ( $a_{i}|i \leq n^{*}$ ) $\subseteq dcl^{eq}$ (a) with $a_{n}*$ = a such that for every $i \leq n*$ , if $p_{i} = tp(a_{i}/{a_{i}|j < i}$ ) then $Aut(p_{i}/Q)$ is type-definable with its action on $p_{i}^{c}$ . A unidimensional simple theory eliminates the quantifier $\exists^{\infty}$ and either interprets (in $C^{eq}$ ) an infinite (...) type-definable group or has the property that ACL(Q) = C for every infinite definable set Q. (shrink)

We lay down the groundwork for the treatment of almost hyperdefinable groups: notions from [5] are put into a natural hierarchy, and new notions, essential to the study to such groups, fit elegantly into this hierarchy. We show that "classical" properties of definable and hyperdefinable groups in simple theories can be generalised to this context. In particular, we prove the existence of stabilisers of Lascar strong types and of the connected and locally connected components of subgroups, and that in (...) a simple one-based theory an almost hyperdefinable group is bounded-by-abelian-by-bounded. (shrink)

In the basic model of Condorcet’s jury theorem and in the literature that follows, an odd-numbered group of voters is assumed so that the simple majority rule can be used. We show that this assumption is not necessary either in Condorcet’s basic model or in the general framework of dichotomous choice. We first apply simple majority rule to an even-numbered homogeneous fixed-size committee. We then provide a justification for using simple majority rule for an even-numbered heterogeneous (...) fixed-size committee when the competence structure of the committee members is not common knowledge. (shrink)

We consider the investigation of the embedding of semigroups in groups, a problem which spans the early-twentieth-century development of abstract algebra. Although this is a simple problem to state, it has proved rather harder to solve, and its apparent simplicity caused some of its would-be solvers to go awry. We begin with the analogous problem for rings, as dealt with by Ernst Steinitz, B. L. van der Waerden and Øystein Ore. After disposing of A. K. Sushkevich’s erroneous contribution in (...) this area, we present A. I. Maltsev’s example of a cancellative semigroup which may not be embedded in a group, which showed for the first time that such an embedding is not possible in general. We then look at the various conditions that were derived for such an embedding to take place: the sufficient conditions of Paul Dubreil and others, and the necessary and sufficient conditions obtained by A. I. Maltsev, Vlastimil Pták and Joachim Lambek. We conclude with some comments on the place of this problem within the theory of semigroups, and also within abstract algebra more generally. (shrink)

We show that if p is a real type which is almost internal in a formula φ in a simple theory, then there is a type p' interalgebraic with a finite tuple of realizations of p, which is generated over φ. Moreover, the group of elementary permutations of p' over all realizations of φ is type-definable.

In this paper, we approach the idea of group cognition from the perspective of the “extended mind” thesis, as a special case of the more general claim that systems larger than the individual human, but containing that human, are capable of cognition (Clark, 2008; Clark & Chalmers, 1998). Instead of deliberating about “the mark of the cognitive” (Adams & Aizawa, 2008), our discussion of group cognition is tied to particular cognitive capacities. We review recent studies of group (...) problem-solving and group memory which reveal that specific cognitive capacities that are commonly ascribed to individuals are also aptly ascribed at the level of groups. These case studies show how dense interactions among people within a group lead to both similarity-inducing and differentiating dynamics that affect the group's ability to solve problems. This supports our claim that groups have organization-dependent cognitive capacities that go beyond the simple aggregation of the cognitive capacities of individuals. Group cognition is thus an emergent phenomenon in the sense of Wimsatt (1986). We further argue that anybody who rejects our strategy for showing that cognitive properties can be instantiated at multiple levels in the organizational hierarchy on a priori grounds is a “demergentist,” and thus incurs the burden of proof for explaining why cognitive properties are “stuck” at a certain level of organizational structure. Finally, we show that our analysis of group cognition escapes the “coupling-constitution” charge that has been leveled against the extended mind thesis (Adams & Aizawa, 2008). (shrink)

We deal with two forms of the "uniqueness cases" in the classification of large simple K*-groups of finite Morley rank of odd type, where large means the 2-rank m2 is at least three. This substantially extends results known for even larger groups having Prüfer 2-rank at least three, so as to cover the two groups PSp 4 and G 2. With an eye towards more distant developments, we carry out this analysis for L*-groups, a context which is substantially broader (...) than the K* setting. (shrink)

An analysis of group justification enables us to understand what it means to say that a research group is justified in making a claim on the basis of evidence. I defend Frederick Schmitt's (1994) joint account of group justification by arguing against a simple summative account of group justification. Also, I respond to two objections to the joint account, one claiming that social epistemologists should always prefer the epistemic value of making true judgments to the (...) epistemic value of maintaining consistency, and another one claiming that the notion of joint commitment implicit in the joint account is epistemically unacceptable. (shrink)

If a group is modelled as a single Bayesian agent, what should its beliefs be? I propose an axiomatic model that connects group beliefs to beliefs of group members, who are themselves modelled as Bayesian agents, possibly with different priors and different information. Group beliefs are proven to take a simple multiplicative form if people’s information is independent, and a more complex form if information overlaps arbitrarily. This shows that group beliefs can incorporate all (...) information spread over the individuals without the individuals having to communicate their (possibly complex and hard-to-describe) private information; communicating prior and posterior beliefs sufices. JEL classification: D70, D71.. (shrink)

This paper completes the proof of the group configuration theorem for simple theories started in [1]. We introduce the notion of an almost hyperdefinable structure, and show that it has a reasonable model theory. We then construct an almost hyperdefinable group from a polygroup chunk.

A study of smooth classes whose generic structures have simple theory is carried out in a spirit similar to Hrushovski 147; Simplicity and the Lascar group, preprint, 1997) and Baldwin–Shi 1). We attach to a smooth class K0, of finite -structures a canonical inductive theory TNat, in an extension-by-definition of the language . Here TNat and the class of existentially closed models of =T+,EX, play an important role in description of the theory of the K0,-generic. We show that (...) if M is the K0,-generic then MEX. Furthermore, if this class is an elementary class then Th=Th). The investigations by Hrushovski and Pillay , provide a general theory for forking and simplicity for the nonelementary classes, and using these ideas, we show that if K0,, where {,*}, has the joint embedding property and is closed under the Independence Theorem Diagram then EX is simple. Moreover, we study cases where EX is an elementary class. We introduce the notion of semigenericity and show that if a K0,-semigeneric structure exists then EX is an elementary class and therefore the -theory of K0,-generic is near model complete. By this result we are able to give a new proof for a theorem of Baldwin and Shelah 1359). We conclude this paper by giving an example of a generic structure whose first-order theory is simple. (shrink)

We prove several results about groups of finite Morley rank without unipotent p-torsion: p-torsion always occurs inside tori, Sylow p-subgroups are conjugate, and p is not the minimal prime divisor of our approximation to the "Weyl group". These results are quickly finding extensive applications within the classification project.

We give examples of (i) a simple theory with a formula (with parameters) which does not fork over [Formula: see text] but has [Formula: see text]-measure 0 for every automorphism invariant Keisler measure [Formula: see text] and (ii) a definable group [Formula: see text] in a simple theory such that [Formula: see text] is not definably amenable, i.e. there is no translation invariant Keisler measure on [Formula: see text]. We also discuss paradoxical decompositions both in the setting (...) of discrete groups and of definable groups, and prove some positive results about small theories, including the definable amenability of definable groups. (shrink)

Group polarization occurs when an initial attitude or belief of individuals becomes more radical after group discussion. Polarization often leads subgroups towards opposite directions. Since the 1960s this effect has been observed and repeatedly confirmed in lab experiments by social psychologists. Persuasive Arguments Theory emerged as the most convincing explanation for this phenomenon. This paper is a first attempt to frame the PAT explanation more formally by means of Bipolar Argumentation Frameworks. In particular, I show that polarization may (...) emerge in a BAF by simple and rational belief updates by participants. (shrink)

We show how the notion of full Frobenius group of finite Morley rank generalizes that of bad group, and how it seems to be more appropriate when we consider the possible existence (still unknown) of nonalgebraic simple groups of finite Morley rank of a certain type, notably with no involution. We also show how these groups appear as a major obstacle in the analysis of FT-groups, if one tries to extend the Feit-Thompson theorem to groups of finite (...) Morley rank. (shrink)

We prove the following theorem. Let G be a connected simple bad group (i.e. of finite Morley rank, nonsolvable and with all the Borel subgroups nilpotent) of minimal Morley rank. Then the Borel subgroups of G are conjugate to each other, and if B is a Borel subgroup of G, then $G = \bigcup_{g \in G}B^g,N_G(B) = B$ , and G has no involutions.

This article may be seen as a summary and a final discussion of the work that the author has done in recent years on the foundation of quantum theory. It is shown that quantum mechanics as a model follows under certain specific conditions from a quite different, much simpler model. This model is connected to the mind of an observer, or to the joint minds of a group of communicating observers. The model is based upon conceptual variables, and an (...) important aspect is that an observer (a group of observers) must decide on which variable to measure. The model is then linked more generally to a theory of decisions. The results are discussed from several angles. (shrink)

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.

We show that R.J. Thompson’s groupsFandTare bi-interpretable with the ring of the integers. From a result by A. Khélif, these groups are quasi-finitely axiomatizable and prime. So, the groupTprovides an example of a simple group which is quasi-finitely axiomatizable and prime. This answers questions posed by T. Altınel and A. Muranov in [2], and by A. Nies in [12].

Dance provides natural conditions for studying relationships between coordination patterns and human experience. von Zimmermann and colleagues investigate whether relatively simple or more complex forms of movement coordination are related to pro‐social experiences during group dance. They find that pro‐social experience depends on the degree to which movement patterns are distributed and diversified, but not the degree to which movement patterns are simply unitary.

Let T be simple, work in Ceq over a boundedly closed set. Let p ∈ S(θ) be internal in a quasi-stably-embedded type-definable set Q (e.g., Q is definable or stably-embedded) and suppose (p, Q) is ACL-embedded in Q (see definitions below). Then Aut(p/Q) with its action on pC is type-definable in Ceq over θ. In particular, if p ∈ S(θ) is internal in a stably-embedded type-definable set Q, and pC υ Q is stably-embedded, then Aut(p/Q) is type-definable with its (...) action on pC. (shrink)

Background Previous reports have described that simple cognitive training using reading aloud and solving simple arithmetic calculations, so-called “learning therapy”, can improve executive functions and processing speed in the older adults. Nevertheless, it is not well-known whether learning therapy improve a wide range of cognitive functions or not. We investigated the beneficial effects of learning therapy on various cognitive functions in healthy older adults. Methods We used a single-blinded intervention with two groups (learning therapy group: LT and (...) waiting list control group: WL). Sixty-four elderly were randomly assigned to LT or WL. In LT, participants performed reading Japanese aloud and solving simple calculations training tasks for 6 months. WL did not participate in the intervention. We measured several cognitive functions before and after 6 months intervention periods. Results Compared to WL, results revealed that LT improved inhibition performance in executive functions (Stroop: LT (Mean = 3.88) vs. WL (Mean = 1.22), adjusted p =.013 and reverse Stroop LT (Mean = 3.22) vs. WL (Mean = 1.59), adjusted p =.015), verbal episodic memory (logical memory: LT (Mean = 4.59) vs. WL (Mean = 2.47), adjusted p =.015), focus attention(D-CAT: LT (Mean = 2.09) vs. WL (Mean = -0.59), adjusted p =.010) and processing speed compared to the waiting list control group (digit symbol coding: LT (Mean = 5.00) vs. WL (Mean = 1.13), adjusted p =.015 and symbol search: LT (Mean = 3.47) vs. WL (Mean = 1.81), adjusted p =.014). Discussion This RCT can showed the benefit of learning therapy on inhibition of executive functions, verbal episodic memory, focus attention, and processing speed in healthy elderly people. Our results were discussed under overlapping hypothesis. Trial registration “This trial was registered in The University Hospital Medical Information Network Clinical Trials Registry (UMIN000006998).”. (shrink)

In a recent issue of Analysis I gave a critique of some arguments made by Di Nucci concerning the so-called Simple View – the view that an agent performs an action intentionally only if he intends so to act. In turn Di Nucci offers a reply that concentrates on two points. The first has to do with a group of examples, one having to do with waking a flatmate, and the others with routine actions such as shifting gears (...) while driving. I rejected these examples, arguing that it is not at all obvious that in them the Simple View is violated. Additionally, I pointed out that these are not cases of agents doing something they thought they could not do, and so have no direct bearing on the issues of practical rationality that motivate Bratman's treatment of the Simple View, which Di Nucci is concerned to defend . Di Nucci accepts this second point. He claims, however, that I failed to understand the dialectic of his argument. …. (shrink)

What are the conditions under which groups of agents will perform well across multiple tasks? The author establishes a set of “alignment conditions” that enforce identity of beliefs and desires across agents. These conditions are necessary and sufficient for ensuring that a multiagent system behaves as if controlled by a rational centralized controller. Several widely observed social phenomena can be understood as facilitating the alignment conditions.

SKOS (Simple Knowledge Organization System) is a recommendation from the World Wide Web Consortium (W3C) for representing controlled vocabularies, taxonomies, thesauri, classifications, and similar systems for organizing and indexing information as linked data elements in the Semantic Web, using the Resource Description Framework (RDF). The SKOS data model is centered on “concepts”, which can have preferred and alternate labels in any language as well as other metadata, and which are identified by addresses on the World Wide Web (URIs). Concepts (...) are grouped into hierarchies through “broader” and “narrower” relations, with “top concepts” at the broadest conceptual level. Concepts are also organized into “concept schemes”, also identified by URIs. Other relations, mappings, and groupings are also supported. This article discusses the history of the development of SKOS and provides notes on adoption, uses, and limitations. (shrink)