We prove the following main theorem: Let be an abstract elementary class satisfying the joint embedding and the amalgamation properties with no maximal models of cardinality μ. Let μ be a cardinal above the the Löwenheim‐Skolem number of the class. If is μ‐Galois‐stable, has no μ‐Vaughtian Pairs, does not have long splitting chains, and satisfies locality of splitting, then any two ‐limits over M, for, are isomorphic over M.

We prove a categoricity transfer theorem for tame abstract elementary classes. Theorem 0.1. Suppose that K is a χ-tame abstract elementary class and satisfies the amalgamation and joint embedding properties and has arbitrarily large models. Let λ ≥ Max{χ.LS(K)⁺}. If K is categorical in λ and λ⁺, then K is categorical in λ⁺⁺. Combining this theorem with some results from [37], we derive a form of Shelah's Categoricity Conjecture for tame abstract elementary classes: Corollary 0.2. Suppose K is a χ-tame (...) abstract elementary class satisfying the amalgamation and joint embedding properties. Let μ₀:= Hanf(K). If χ ≤ ‮ב‬(2μ0)+ and K is categorical in some λ⁺ > ‮ב‬(2μ0)+, then K is categorical in μ for all μ > ‮ב‬(2μ0)+. (shrink)

We prove that from categoricity in λ+ we can get categoricity in all cardinals ≥ λ+ in a χ-tame abstract elementary classe [Formula: see text] which has arbitrarily large models and satisfies the amalgamation and joint embedding properties, provided [Formula: see text] and λ ≥ χ. For the missing case when [Formula: see text], we prove that [Formula: see text] is totally categorical provided that [Formula: see text] is categorical in [Formula: see text] and [Formula: see text].

We present Saharon Shelah's Stability Spectrum and Homogeneity Spectrum theorems, as well as the equivalence between the order property and instability in the framework of Finite Diagrams. Finite Diagrams is a context which generalizes the first order case. Localized versions of these theorems are presented. Our presentation is based on several papers; the point of view is contemporary and some of the proofs are new. The treatment of local stability in Finite Diagrams is new.

We introduce tame abstract elementary classes as a generalization of all cases of abstract elementary classes that are known to permit development of stability-like theory. In this paper, we explore stability results in this new context. We assume that [Formula: see text] is a tame abstract elementary class satisfying the amalgamation property with no maximal model. The main results include:. Theorem 0.1. Suppose that [Formula: see text] is not only tame, but [Formula: see text]-tame. If [Formula: see text] and [Formula: (...) see text] is Galois stable in μ, then [Formula: see text], where [Formula: see text] is a relative of κ from first order logic. [Formula: see text] is the Hanf number of the class [Formula: see text]. It is known that [Formula: see text]. The theorem generalizes a result from [17]. It is used to prove both the existence of Morley sequences for non-splitting and the following initial step towards a stability spectrum theorem for tame classes:. Theorem 0.2. If [Formula: see text] is Galois-stable in some [Formula: see text], then [Formula: see text] is stable in every κ with κμ=κ. For example, under GCH we have that [Formula: see text] Galois-stable in μ implies that [Formula: see text] is Galois-stable in μ+n for all n < ω. (shrink)

We present a self-contained exposition of the basic aspects of simple theories while developing the fundamentals of forking calculus. We expound also the deeper aspects of S. Shelah's 1980 paper Simple unstable theories. The concept of weak dividing has been replaced with that of forking. The exposition is from a contemporary perspective and takes into account contributions due to S. Buechler, E. Hrushovski, B. Kim, O. Lessmann, S. Shelah and A. Pillay.

Let κ and λ be infinite cardinals such that κ ≤ λ (we have new information for the case when $\kappa ). Let T be a theory in L κ +, ω of cardinality at most κ, let φ(x̄, ȳ) ∈ L λ +, ω . Now define $\mu^\ast_\varphi (\lambda, T) = \operatorname{Min} \{\mu^\ast:$ If T satisfies $(\forall\mu \kappa)(\exists M_\chi \models T)(\exists \{a_i: i Our main concept in this paper is $\mu^\ast_\varphi (\lambda, \kappa) = \operatorname{Sup}\{\mu^\ast(\lambda, T): T$ is a theory (...) in L κ +, ω of cardinality κ at most, and φ (x, y) ∈ L λ +, ω }. This concept is interesting because of THEOREM 1. Let $T \subseteq L_{\kappa^+,\omega}$ of cardinality ≤ κ, and φ (x̄, ȳ) ∈ L λ +, ω . If $(\forall\mu then $(\forall_\chi > \kappa) I(\chi, T) = 2^\chi$ (where I(χ, T) stands for the number of isomorphism types of models of T of cardinality χ). Many years ago the second author proved that $\mu^\ast (\lambda, \kappa) \leq \beth_{(2^\lambda)^+}$ . Here we continue that work by proving. THEOREM 2. $\mu^\ast (\lambda, \aleph_0) = \beth_{\lambda^+}$ . THEOREM 3. For every κ ≤ λ we have $\mu^\ast (\lambda, \kappa) \leq \beth)_{(\lambda^\kappa)}^+$ . For some κ or λ we have better bounds than in Theorem 3, and this is proved via a new two cardinal theorem. THEOREM 4. For every $\kappa \leq \lambda, T \subseteq L_{\kappa^+,\omega}$ , and any set of formulas $\Lambda \subseteq L_{\lambda^+,\omega}$ such that $\Lambda \subseteq L_{\kappa^+,\omega}$ , if T is (Λ,μ)-unstable for μ satisfying μ μ * (λ, κ) = μ then T is Λ-unstable (i.e. for every χ ≥ λ, T is (Λ, χ)-unstable). Moreover, T is L κ +, ω -unstable. In the second part of the paper, we show that always in the applications it is possible to replace the function I(χ, T) by the function IE(χ, T), and we give an application of the theorems to Boolean powers. (shrink)

The new result of this paper is that for θ-stable we have S1[θ] = D[θ, L, ∞]. S1 is Hrushovski's rank. This is an improvement of a result of Kim and Pillay, who for simple theories under the assumption that either of the ranks be finite obtained the same identity. Only the first equality is new, the second equality is a result of Shelah from the seventies. We derive it by studying localizations of several rank functions, we get the followingMain (...) Theorem. Suppose that μ is regular satisfying μ ≥ |T|+, p is a finite type, and Δ is a set of formulas closed under Boolean operations. If either R[p, Δ, μ+] < ∞ or p is Δ-stable and μ satisfies “for every sequence {μi : i < |Δ| + ℵ0} of cardinals μi < μ we have that equation image holds”, then S[p, Δ, μ+] = D[p, Δ, μ+] = R[p, Δ, μ+].The S rank above is a localized version of Hrushovski's S1 rank. This rank, as well as our systematic use of local stability, allows us to get a more conceptual proof of the equality of D and R, which is an old result of Shelah. A particular case of the theorem offers a new sufficient condition for the equality of S1 and D[·, L, ∞]. We also manage, due to a more general approach, to avoid some combinatorial difficulties present in Shelah's original exposition. (shrink)

Let M be a given model with similarity type L = L(M), and let L' be any fragment of L |L(M)| +, ω of cardinality |L(M)|. We call $N \prec M L'$ -relatively saturated $\operatorname{iff}$ for every $B \subseteq N$ of cardinality less than | N | every L'-type over B which is realized in M is realized in M is realized in N. We discuss the existence of such submodels. The following are corollaries of the existence theorems. (1) If (...) M is of cardinality at least $\beth_{\omega_1}$ , and fails to have the ω order property, then there exists $N \prec M$ which is relatively saturated in M of cardinality $\beth_{\omega_1}$ . (2) Assume GCH. Let ψ ∈ L_{ω_1, ω, and let $L' \subseteq L_{\omega 1, \omega$ be a countable fragment containing ψ. If $\exists \chi > \aleph_0$ such that $I(\chi, \psi) , then for every $M \models \psi$ and every cardinal $\lambda of uncountable cofinality, M has an L'-relatively saturated submodel of cardinality λ. (shrink)

. We study a local version of the order property in several frameworks, with an emphasis on frameworks where the compactness theorem fails: (1) Inside a fixed model, (2) for classes of models where the compactness theorem fails and (3) for the first order case. Appropriate localizations of the order property, the independence property, and the strict order property are introduced. We are able to generalize some of the results that were known in the case of local stability for the (...) first order theories, and for stability for nonelementary classes (existence of indiscernibles, existence of averages, stability spectrum, equivalence between order and instability). In the first order case, we also prove the local version of Shelah's Trichotomy Theorem. Finally, as an application, we give a new characterization of stable types when the ambient first order theory is simple. (shrink)

Basic results on the model theory of substructures of a fixed model are presented. The main point is to avoid the use of the compactness theorem, so this work can easily be applied to the model theory of L ω 1 ,ω and its relatives. Among other things we prove the following theorem: Let M be a model, and let λ be a cardinal satisfying λ |L(M)| = λ. If M does not have the ω-order property, then for every $A (...) \subseteq M, |A| \leq \lambda$ , and every $\mathbf{I} \subseteq M$ of cardinality λ + there exists $\mathbf{J} \subseteq \mathbf{I}$ of cardinality λ + which is an indiscernible set over A. This is an improvement of a result of S. Shelah. (shrink)

We present a downward Löwenheim-Skolem theorem which transfers downward formulas from L ∞,ω to L κ +, ω . The simplest instance is: Theorem 1. Let $\lambda > \kappa$ be infinite cardinals, and let L be a similarity type of cardinality κ at most. For every L-structure M of cardinality λ and every $X \subseteq M$ there exists a model $N \prec M$ containing the set X of power |X| · κ such that for every pair of finite sequences a, (...) b ∈ N $\langle N, \mathbf{a}\rangle \equiv_{\| N \|^+,\omega} \langle N, \mathbf{b}\rangle \Leftrightarrow \langle M, \mathbf{a}\rangle \equiv_{\infty,\omega} \langle M, \mathbf{b}\rangle.$ The following theorem is an application: Theorem 2. Let $\lambda , and suppose χ is a Ramsey cardinal greater than λ. If T has the (χ, L κ +, ω -unsuperstability property, then T has the (χ, L λ +, ω )-unsuperstability property. (shrink)

Let L(Q) be first order logic with Keisler's quantifier, in the λ + interpretation (= the satisfaction is defined as follows: $M \models (\mathbf{Q}x)\varphi(x)$ means there are λ + many elements in M satisfying the formula φ(x)). Theorem 1. Let λ be a singular cardinal; assume □ λ and GCH. If T is a complete theory in L(Q) of cardinality at most λ, and p is an L(Q) 1-type so that T strongly omits $p (= p$ has no support, to (...) be defined in $\S1$ ), then T has a model of cardinality λ + in the λ + interpretation which omits p. Theorem 2. Let λ be a singular cardinal, and let T be a complete first order theory of cardinality λ at most. Assume □ λ and GCH. If Γ is a smallness notion then T has a model of cardinality λ + such that a formula φ(x) is realized by λ + elements of M iff φ(x) is not Γ-small. The theorem is proved also when λ is regular assuming $\lambda = \lambda^{ . It is new when λ is singular or when |T| = λ is regular. Theorem 3. Let λ be singular. If $\operatorname{Con}(ZFC + GCH + (\exists\kappa)$ [κ is a strongly compact cardinal]), then the following in consistent: ZFC + GCH + the conclusions of all above theorems are false. (shrink)

We define a rich model to be one which contains a proper elementary substructure isomorphic to itself. Existence, nonstructure, and categoricity theorems for rich models are proved. A theory T which has fewer than $\min(2^\lambda,\beth_2)$ rich models of cardinality $\lambda(\lambda > |T|)$ is totally transcendental. We show that a countable theory with a unique rich model in some uncountable cardinal is categorical in ℵ 1 and also has a unique countable rich model. We also consider a stronger notion of richness, (...) and use it to characterize superstable theories. (shrink)

$\underline{\text{Saturation is} (\mu, \kappa)-\text{transferable in} T}$ if and only if there is an expansion T 1 of T with ∣ T 1 ∣ = ∣ T ∣ such that if M is a μ-saturated model of T 1 and ∣ M ∣ ≥ κ then the reduct M ∣ L(T) is κ-saturated. We characterize theories which are superstable without f.c.p., or without f.c.p. as, respectively those where saturation is (ℵ 0 , λ)- transferable or (κ (T), λ)-transferable for all λ. (...) Further if for some $\mu \geq \mid T \mid, 2^\mu > \mu^+$ , stability is equivalent to for all μ ≥ ∣ T ∣, saturation is (μ, 2 μ )- transferable. (shrink)

How does your mind work? How does your brain give rise to your mind? These are questions that all of us have wondered about at some point in our lives, if only because everything that we know is experienced in our minds. They are also very hard questions to answer. After all, how can a mind understand itself? How can you understand something as complex as the tool that is being used to understand it? This book provides an introductory and (...) self-contained description of some of the exciting answers to these questions that modern theories of mind and brain have recently proposed. Stephen Grossberg is broadly acknowledged to be the most important pioneer and current research leader who has, for the past 50 years, modelled how brains give rise to minds, notably how neural circuits in multiple brain regions interact together to generate psychological functions. This research has led to a unified understanding of how, where, and why our brains can consciously see, hear, feel, and know about the world, and effectively plan and act within it. The work embodies revolutionary Principia of Mind that clarify how autonomous adaptive intelligence is achieved. It provides mechanistic explanations of multiple mental disorders, including symptoms of Alzheimer's disease, autism, amnesia, and sleep disorders; biological bases of morality and religion, including why our brains are biased towards the good so that values are not purely relative; perplexing aspects of the human condition, including why many decisions are irrational and self-defeating despite evolution's selection of adaptive behaviors; and solutions to large-scale problems in machine learning, technology, and Artificial Intelligence that provide a blueprint for autonomously intelligent algorithms and robots. Because brains embody a universal developmental code, unifying insights also emerge about shared laws that are found in all living cellular tissues, from the most primitive to the most advanced, notably how the laws governing networks of interacting cells support developmental and learning processes in all species. The fundamental brain design principles of complementarity, uncertainty, and resonance that Grossberg has discovered also reflect laws of the physical world with which our brains ceaselessly interact, and which enable our brains to incrementally learn to understand those laws, thereby enabling humans to understand the world scientifically. Accessibly written, and lavishly illustrated, Conscious Mind/Resonant Brain is the magnum opus of one of the most influential scientists of the past 50 years, and will appeal to a broad readership across the sciences and humanities. (shrink)

Scholars studying the global diffusion of “corporate social responsibility” (CSR) practices and the associated rise of privatized forms of economic governance have tended to shift attention away from the role of corporations in motivating these processes to the one played by nonbusiness forces seeking social control of corporations. We bring corporate power back in by turning the spotlight to the agency of business classes, the business entities capable of pursuing transcorporate, societal-level, macro-political endeavors. Building on a comparative investigation of two (...) of the world’s earliest mass CSR adoptions, in postwar Venezuela and Britain, we argue that business classes responding to anti-capitalist challenges were the original diffusers of CSR practices and, interrelatedly, promoters of CSR-based, privatized forms of regulation and governance. Organized by peak business associations, the purpose of these “business-class CSR mobilizations” was to weaken the state in its relation to corporations and increase the control of business over social trends. We discuss the contribution of our historical perspective and analytical approach to a more complete and balanced picture of the global rise of CSR in late capitalism. (shrink)

A natural starting point for theories of perceptual states is ordinary perception, in which a subject is successfully related to her mind-independent surroundings. Correspondingly, the simplest theory of perceptual states models all such states on perception. Typically, this simple, common-factor relational view of perceptual states has received a perfunctory dismissal on the grounds that hallucinations are nonperceptual. But I argue that the nonperceptual view of hallucinations has been accepted too quickly. I consider three observations thought to support the view, and (...) argue that all three are dealt with equally well by an alternative view, illusionism, on which hallucinations do involve perception. Since this is so, adopting a common-factor relational view of all perceptual states remains a tenable option. (shrink)

Luck (2009) argues that gamers face a dilemma when it comes to performing certain virtual acts. Most gamers regularly commit acts of virtual murder, and take these acts to be morally permissible. They are permissible because unlike real murder, no one is harmed in performing them; their only victims are computer-controlled characters, and such characters are not moral patients. What Luck points out is that this justification equally applies to virtual pedophelia, but gamers intuitively think that such acts are not (...) morally permissible. The result is a dilemma: either gamers must reject the intuition that virtual pedophelic acts are impermissible and so accept partaking in such acts, or they must reject the intuition that virtual murder acts are permissible, and so abstain from many (if not most) extant games. While the prevailing solution to this dilemma has been to try and find a morally relevant feature to distinguish the two cases, I argue that a different route should be pursued. It is neither the case that all acts of virtual murder are morally permissible, nor are all acts of virtual pedophelia impermissible. Our intuitions falter and produce this dilemma because they are not sensitive to the different contexts in which games present virtual acts. (shrink)

Our sense of entitlement influences our interactions and attitudes in a range of specific relational contexts, one of them being aging parents’ relationships with their adult children. This study aimed to examine the factor structure of the Sense of Relational Entitlement—aging parents toward their offspring, an 11-item questionnaire that assesses aging people’s sense of relational entitlement toward their children, and examine the associations of its subscales with related personality and mental health constructs. One thousand and six participants, aged 65–99, with (...) at least one child, completed the SRE-ao, Brief Symptom Inventory, Loneliness Scale, and General Belongingness scale. The SRE-ao demonstrated good construct structure using confirmatory factor analysis. Both SRE-ao subscales were significantly and positively associated with anxiety, depression, somatization and sense of loneliness and negatively with sense of belonging. When all variables were entered into a regression model, age, anxiety, and low sense of belonging, but not sense of loneliness, positively predicted both restricted and inflated sense of entitlement. Somatization negatively predicted inflated sense of entitlement. The SRE-ao is a reliable and valid scale that can be used in clinical practice and research to enhance our understanding of parent–child relationships throughout the lifespan. (shrink)

This paper presents the design and development of intelligent tutoring system for teaching Oracle. The Oracle Intelligent Tutoring System (OITS) examined the power of a new methodology to supporting students in Oracle programming. The system presents the topic of Introduction to Oracle with automatically generated problems for the students to solve. The system is dynamically adapted at run time to the student’s individual progress. An initial evaluation study was done to investigate the effect of using the intelligent tutoring system on (...) the performance of students. (shrink)

How do we assign values to virtual items, which include virtual objects, properties, events, subjects, worlds, environments, and experiences? In this article, I offer a framework for answering this question. After considering different value theses in the literature, I argue that whether we think these theses mutually exclusive or not turns on our view about the number of value-salient kinds virtual items belong to. Virtual monism is the view that virtual Xs belong to only one value-salient kind in relation to (...) X. Virtual pluralism is the view that they belong to more than one value-salient kind. I argue for two claims. First, virtual monism is mistaken. Minimally some virtual Xs are Xs, while others are not. Second, dualistic virtual pluralism is also mistaken because it is too coarse grained. Instead, I argue for fourfold pluralism: virtual items either represent an original's properties or reproduce essential properties and do so to lesser or greater extents. This gives us four value-salient kinds of virtual X: virtual reproductions, simulations, representations, and simulacra of X. I apply this view to various debates in the literature and conclude with a discussion of less basic hybrid kinds. (shrink)

Un paralelismo antitetico le da forma a los fragmentos de los Pensamientos de Blaise Pascal, al prolongar el movimiento paradojico de la naturaleza humana desde el divertissement hasta los porticos de la conversion. En el primer foco de la figura, la diversion, contemplada de un modo alegorico, por la cual el hombre se aleja de Dios y hace del mundo el objeto de su concupiscencia. En el otro foco, la conversion, en la que el hombre se aleja del mundo y (...) se vuelve a Dios merced a un movimiento de la Gracia. La concupiscencia es el enves del orden de la Caridad, como el divertimento es el reverso de la partida que abre a la fe cristiana. Las paginas de este libro retratan el trayecto del unico jugador y dan razon de la complejidad de su existencia, que se debate entre el tedio, la angustia ante la muerte y el riesgo de una apuesta en la que la libertad empena el todo de su nada en vistas a una ganancia infinita. (shrink)

The gamer’s dilemma offers three plausible but jointly inconsistent premises: (1) Virtual murder in video games is morally permissible. (2) Virtual paedophelia in video games is not morally permissible. (3) There is no morally relevant difference between virtual murder and virtual paedophelia in video games. In this paper I argue that the gamer’s dilemma can be understood as one of three distinct dilemmas, depending on how we understand two key ideas in Morgan Luck’s (2009) original formulation. The two ideas are (...) those of (1) occurring in a video game and (2) being a virtual instance of murder or paedophelia. Depending on the weight placed on the gaming context, the dilemma is either about in-game acts or virtual acts. And depending on the type of virtual acts we have in mind, the dilemma is either about virtual representations or virtual partial reproductions of murder and paedophelia. This gives us three dilemmas worth resolving: a gaming dilemma, a representation dilemma, and a simulation dilemma. I argue that these dilemmas are about different issues, apply to different cases, and are susceptible to different solutions. I also consider how different participants in the debate have interpreted the dilemma in one or more of these three ways. (shrink)

Several recent accounts of modeling have focused on the modal dimension of scientific inquiry. More precisely, it has been suggested that there are specific models and modeling practices that are best understood as being geared towards possibilities, a view recently dubbed modal modeling. But modalities encompass much more than mere possibility claims. Besides possibilities, modal modeling can also be used to investigate contingencies, necessities or impossibilities. Although these modal concepts are logically connected to the notion of possibility, not all models (...) are equal in their affordances for these richer modal inferences. This paper investigates the modal extent of selected models and argues that analyzing singular model-target pairings by themselves is typically not enough to explain their modal aptness or to identify the kinds of modalities they can be used to reason about. Furthermore, it is argued that some important concepts that are not explicitly modal - like biological robustness - can be understood modally through their relational nature to a background space of possibilities. In conclusion, it is suggested that the strategy of modal modeling is contrastive, situating particular possibilities in larger modal spaces and studying the structural relations within them. (shrink)

Recently, several critics of the multiple realizability thesis have argued that philosophers have tended to accept the thesis on too weak grounds. On the one hand, the analytic challenge has problematized how philosophers have treated the multiple realization relation itself, claiming that assessment of the sameness of function and the relevant difference of realizers has been uncritical. On the other hand, it is argued that the purported evidence of the thesis is often left empirically unverified. This paper provides a novel (...) strategy to answer these worries by introducing a role for multiple realizability in the context of biological engineering. In the field of synthetic biology, bioengineers redesign the evolutionary realizations of biological functions, even constructing artificial chemical surrogates in the laboratory. I show how in the rational design approach to biological engineering, multiple realizability can function as a design heuristic in which the sameness of function and difference of realizers can be controlled. Although practically motivated, this engineering approach has also a theoretical, exploratory component that can be used to study the empirical limitations of multiple realizability. Successful realization of the engineering designs would amount to a concrete demonstration of multiple realizability, taking evidence for MRT beyond what is readily found in nature. (shrink)

Critics of multiple realizability have recently argued that we should concentrate solely on actual here-and-now realizations that are found in nature. The possibility of alternative, but unactualized, realizations is regarded as uninteresting because it is taken to be a question of pure logic or an unverifiable scenario of science fiction. However, in the biological context only a contingent set of realizations is actualized. Drawing on recent work on the theory of neutral biological spaces, the paper shows that we can have (...) ways of assessing the modal dimension of multiple realizability that do not have to rely on mere conceivability. (shrink)