Results for ' pseudofinite dimension'

971 found
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  1.  39
    Pseudofinite difference fields and counting dimensions.Tingxiang Zou - 2021 - Journal of Mathematical Logic 21 (1):2050022.
    We study a family of ultraproducts of finite fields with the Frobenius automorphism in this paper. Their theories have the strict order property and TP2. But the coarse pseudofinite dimension of the definable sets is definable and integer-valued. Moreover, we also discuss the possible connection between coarse dimension and transformal transcendence degree in these difference fields.
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  2.  1
    Dimension and Measure in Pseudofinite H-Structures.Alexander Berenstein, Darío García & Z. O. U. Tingxiang - 2025 - Journal of Symbolic Logic 90 (1):68-104.
    We study H-structures associated with $SU$ -rank 1 measurable structures. We prove that the $SU$ -rank of the expansion is continuous and that it is uniformly definable in terms of the parameters of the formulas. We also introduce notions of dimension and measure for definable sets in the expansion and prove they are uniformly definable in terms of the parameters of the formulas.
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  3.  16
    Pseudofinite Structures and Counting Dimensions.Tingxiang Zou - 2021 - Bulletin of Symbolic Logic 27 (2):223-223.
    The thesis pseudofinite structures and counting dimensions is about the model theory of pseudofinite structures with the focus on groups and fields. The aim is to deepen our understanding of how pseudofinite counting dimensions can interact with the algebraic properties of underlying structures and how we could classify certain classes of structures according to their counting dimensions. Our approach is by studying examples. We treat three classes of structures: The first one is the class of H-structures, which (...)
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  4.  28
    Pseudofinite groups and VC-dimension.Gabriel Conant & Anand Pillay - 2020 - Journal of Mathematical Logic 21 (2):2150009.
    We develop “local NIP group theory” in the context of pseudofinite groups. In particular, given a sufficiently saturated pseudofinite structure G expanding a group, and left invariant NIP formula δ...
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  5.  31
    (1 other version)Pseudofinite difference fields.Tingxiang Zou - 2019 - Journal of Mathematical Logic 19 (2):1950011.
    We study a family of ultraproducts of finite fields with the Frobenius automorphism in this paper. Their theories have the strict order property and TP2. But the coarse pseudofinite dimension of the definable sets is definable and integer-valued. Moreover, we establish a partial connection between coarse dimension and transformal transcendence degree in these difference fields.
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  6.  86
    Pseudofinite structures and simplicity.Darío García, Dugald Macpherson & Charles Steinhorn - 2015 - Journal of Mathematical Logic 15 (1):1550002.
    We explore a notion of pseudofinite dimension, introduced by Hrushovski and Wagner, on an infinite ultraproduct of finite structures. Certain conditions on pseudofinite dimension are identified that guarantee simplicity or supersimplicity of the underlying theory, and that a drop in pseudofinite dimension is equivalent to forking. Under a suitable assumption, a measure-theoretic condition is shown to be equivalent to local stability. Many examples are explored, including vector spaces over finite fields viewed as 2-sorted finite (...)
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  7.  26
    Dividing and weak quasi-dimensions in arbitrary theories.Isaac Goldbring & Henry Towsner - 2015 - Archive for Mathematical Logic 54 (7-8):915-920.
    We show that any countable model of a model complete theory has an elementary extension with a “pseudofinite-like” quasi-dimension that detects dividing.
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  8.  21
    Dimensional Groups and Fields.Frank O. Wagner - 2020 - Journal of Symbolic Logic 85 (3):918-936.
    We shall define a general notion of dimension, and study groups and rings whose interpretable sets carry such a dimension. In particular, we deduce chain conditions for groups, definability results for fields and domains, and show that a pseudofinite$\widetilde {\mathfrak M}_c$-group of finite positive dimension contains a finite-by-abelian subgroup of positive dimension, and a pseudofinite group of dimension 2 contains a soluble subgroup of dimension 2.
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  9.  17
    Countable models of the theories of baldwin–shi hypergraphs and their regular types.Danul K. Gunatilleka - 2019 - Journal of Symbolic Logic 84 (3):1007-1019.
    We continue the study of the theories of Baldwin–Shi hypergraphs from [5]. Restricting our attention to when the rank δ is rational valued, we show that each countable model of the theory of a given Baldwin–Shi hypergraph is isomorphic to a generic structure built from some suitable subclass of the original class used in the construction. We introduce a notion of dimension for a model and show that there is a an elementary chain $\left\{ {\mathfrak{M}_\beta :\beta \leqslant \omega } (...)
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  10. Bourdieu's Theory of Cultural Change: Explication, Application, Critique.Dimensions of Cultural Change & Supply Vs Demand - 2002 - Sociological Theory 20 (2).
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  11. The call of the wild?Artificial Lives & Philosophical Dimensions Of Farm - 1995 - In T. B. Mepham, Gregory A. Tucker & Julian Wiseman, Issues in agricultural bioethics. Nottingham: Nottingham University Press.
     
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  12.  54
    Pseudofinite and Pseudocompact Metric Structures.Isaac Goldbring & Vinicius Cifú Lopes - 2015 - Notre Dame Journal of Formal Logic 56 (3):493-510.
    The definition of a pseudofinite structure can be translated verbatim into continuous logic, but it also gives rise to a stronger notion and to two parallel concepts of pseudocompactness. Our purpose is to investigate the relationship between these four concepts and establish or refute each of them for several basic theories in continuous logic. Pseudofiniteness and pseudocompactness turn out to be equivalent for relational languages with constant symbols, and the four notions coincide with the standard pseudofiniteness in the case (...)
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  13.  18
    Pseudofiniteness in Hrushovski Constructions.Ali N. Valizadeh & Massoud Pourmahdian - 2020 - Notre Dame Journal of Formal Logic 61 (1):1-10.
    In a relational language consisting of a single relation R, we investigate pseudofiniteness of certain Hrushovski constructions obtained via predimension functions. It is notable that the arity of the relation R plays a crucial role in this context. When R is ternary, by extending the methods recently developed by Brody and Laskowski, we interpret 〈Q+,<〉 in the 〈K+,≤∗〉-generic and prove that this structure is not pseudofinite. This provides a negative answer to the question posed in an earlier work by (...)
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  14.  13
    Counting in Uncountably Categorical Pseudofinite Structures.Alexander van Abel - 2024 - Journal of Symbolic Logic 89 (4):1455-1475.
    We show that every definable subset of an uncountably categorical pseudofinite structure has pseudofinite cardinality which is polynomial (over the rationals) in the size of any strongly minimal subset, with the degree of the polynomial equal to the Morley rank of the subset. From this fact, we show that classes of finite structures whose ultraproducts all satisfy the same uncountably categorical theory are polynomial R-mecs as well as N-dimensional asymptotic classes, where N is the Morley rank of the (...)
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  15.  20
    Pseudofinite h-structures and groups definable in supersimple h-structures.Tingxiang Zou - 2019 - Journal of Symbolic Logic 84 (3):937-956.
    In this article we explore some properties of H-structures which are introduced in [2]. We describe a construction of H-structures based on one-dimensional asymptotic classes which preserves pseudofiniteness. That is, the H-structures we construct are ultraproducts of finite structures. We also prove that under the assumption that the base theory is supersimple of SU-rank one, there are no new definable groups in H-structures. This improves the corresponding result in [2].
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  16.  26
    Disjoint $n$ -Amalgamation and Pseudofinite Countably Categorical Theories.Alex Kruckman - 2019 - Notre Dame Journal of Formal Logic 60 (1):139-160.
    Disjoint n-amalgamation is a condition on a complete first-order theory specifying that certain locally consistent families of types are also globally consistent. In this article, we show that if a countably categorical theory T admits an expansion with disjoint n-amalgamation for all n, then T is pseudofinite. All theories which admit an expansion with disjoint n-amalgamation for all n are simple, but the method can be extended, using filtrations of Fraïssé classes, to show that certain nonsimple theories are (...). As case studies, we examine two generic theories of equivalence relations, Tfeq∗ and TCPZ, and show that both are pseudofinite. The theories Tfeq∗ and TCPZ are not simple, but they have NSOP1. This is established here for TCPZ for the first time. (shrink)
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  17. Omega-Categorical Pseudofinite Groups.Dugald Macpherson & Katrin Tent - forthcoming - Journal of Symbolic Logic:1-14.
    We explore the interplay between $\omega $ -categoricity and pseudofiniteness for groups, and we conjecture that $\omega $ -categorical pseudofinite groups are finite-by-abelian-by-finite. We show that the conjecture reduces to nilpotent p-groups of class 2, and give a proof that several of the known examples of $\omega $ -categorical p-groups satisfy the conjecture. In particular, we show by a direct counting argument that for any odd prime p the ( $\omega $ -categorical) model companion of the theory of nilpotent (...)
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  18.  67
    On algebraic closure in pseudofinite fields.Özlem Beyarslan & Ehud Hrushovski - 2012 - Journal of Symbolic Logic 77 (4):1057-1066.
    We study the automorphism group of the algebraic closure of a substructure A of a pseudofinite field F. We show that the behavior of this group, even when A is large, depends essentially on the roots of unity in F. For almost all completions of the theory of pseudofinite fields, we show that over A, algebraic closure agrees with definable closure, as soon as A contains the relative algebraic closure of the prime field.
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  19.  1
    The Dimensions and the Affinities of the Game.Ramona Nicoleta Arieșan - 2018 - Studia Universitatis Babeş-Bolyai Philosophia:85-94.
    The Dimensions and the Affinities of the Game. Two people cannot be replicated. But they can have common points in life, such as social aspects or others regarding their sentimental life, their artistical one, their spiritual one and from these we can see how everything comes into place and forms their unicity. It evolves on their personal style, on the character, perceptions, visions and also in the person they aim to be. So, the game expresses, no matter what dimension (...)
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  20. Dimensions of Animal Consciousness.Jonathan Birch, Alexandra K. Schnell & Nicola S. Clayton - 2020 - Trends in Cognitive Sciences 24 (10):789-801.
    How does consciousness vary across the animal kingdom? Are some animals ‘more conscious’ than others? This article presents a multidimensional framework for understanding interspecies variation in states of consciousness. The framework distinguishes five key dimensions of variation: perceptual richness, evaluative richness, integration at a time, integration across time, and self-consciousness. For each dimension, existing experiments that bear on it are reviewed and future experiments are suggested. By assessing a given species against each dimension, we can construct a consciousness (...)
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  21.  38
    Model theory of finite and pseudofinite groups.Dugald Macpherson - 2018 - Archive for Mathematical Logic 57 (1-2):159-184.
    This is a survey, intended both for group theorists and model theorists, concerning the structure of pseudofinite groups, that is, infinite models of the first-order theory of finite groups. The focus is on concepts from stability theory and generalisations in the context of pseudofinite groups, and on the information this might provide for finite group theory.
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  22. Dimensions of Value.Brian Hedden & Daniel Muñoz - 2024 - Noûs 58 (2):291-305.
    Value pluralists believe in multiple dimensions of value. What does betterness along a dimension have to do with being better overall? Any systematic answer begins with the Strong Pareto principle: one thing is overall better than another if it is better along one dimension and at least as good along all others. We defend Strong Pareto from recent counterexamples and use our discussion to develop a novel view of dimensions of value, one which puts Strong Pareto on firmer (...)
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  23.  24
    First-order recognizability in finite and pseudofinite groups.Yves Cornulier & John S. Wilson - 2020 - Journal of Symbolic Logic 85 (2):852-867.
    It is known that there exists a first-order sentence that holds in a finite group if and only if the group is soluble. Here it is shown that the corresponding statements with ‘solubility’ replaced by ‘nilpotence’ and ‘perfectness’, among others, are false.These facts present difficulties for the study of pseudofinite groups. However, a very weak form of Frattini’s theorem on the nilpotence of the Frattini subgroup of a finite group is proved for pseudofinite groups.
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  24.  39
    Epistemic Dimensions of Personhood, by Simon Evnine.P. Baumann - 2009 - Mind 118 (471):823-827.
    Review of Evnine, "Epistemic Dimensions of Personhood".
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  25.  38
    Notice of Retraction: Pseudofinite difference field.Tingxiang Zou - forthcoming - Journal of Mathematical Logic:1993001.
    Journal of Mathematical Logic, Ahead of Print.
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  26.  25
    The Dimensions of Paulinian Stewardship.Allan P. M. Lappay - 2022 - European Journal of Theology and Philosophy 2 (3):1-2.
    In this treatise, the dimensions of Paulinian stewardship as a way of caring for God’s creation are expounded and analyzed. This is ensued by a critical review on the Epistles of St. Paul in explaining the concept of stewardship as a calling, leading by example, and a way of life. Moreover, as stewardship is equated with the Paulinian core value of community, the attitude, and the action of a steward’s life of service to others and God are highlighted.
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  27.  71
    Dimension‐Based Statistical Learning Affects Both Speech Perception and Production.Matthew Lehet & Lori L. Holt - 2017 - Cognitive Science 41 (S4):885-912.
    Multiple acoustic dimensions signal speech categories. However, dimensions vary in their informativeness; some are more diagnostic of category membership than others. Speech categorization reflects these dimensional regularities such that diagnostic dimensions carry more “perceptual weight” and more effectively signal category membership to native listeners. Yet perceptual weights are malleable. When short-term experience deviates from long-term language norms, such as in a foreign accent, the perceptual weight of acoustic dimensions in signaling speech category membership rapidly adjusts. The present study investigated whether (...)
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  28. La dimensión estética y antropológica del juego en Friedrich Schiller y José Ortega y Gasset / The Aesthetic and Anthropological Dimension of Play in Friedrich Schiller and José Ortega y Gasset.Inmaculada Murcia Serrano - 2013 - Laguna 32:27-42.
    La insistencia de Ortega y Gasset en la dimensión lúdica de la vida, tan opuesta a la trágica de Unamuno, ha sido analizada desde diferentes puntos de vista. Sin embargo, apenas se ha tenido en consideración la influencia que pudo tener la reflexión filosófica de Friedrich Schiller, quien hizo del juego la clave de la educación ilustrada del hombre y del logro de una vida plena. Con este presupuesto, se someten a examen dos textos fundamentales de Ortega, El tema de (...)
     
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  29.  29
    Dimensions of majority rule.Ogan Yumlu - 2019 - Philosophy and Social Criticism 45 (4):527-536.
    The principle of majority rule is a concept that is often employed both in normative democratic theory and in practical politics. But not only that there are relatively few academic studies focusing exclusively on this concept, it is also possible to claim that the existing discussions usually overlook different dimensions of majority rule. This article aims to outline some suggestions for what these dimensions might be, such as: the nature of the participants, the subject matter of the decision and the (...)
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  30.  16
    Epistemological dimensions of evolutionary psychology.Thiemo Breyer (ed.) - 2014 - New York: Springer.
    ​​​​​As psychology and philosophy arose as answers to the eternal question of how the mind works, evolutionary psychology has gained ground over recent years as a link between cognitive-behavioral and natural-science theories of the mind. This provocative field has also gathered a wide range of criticisms, from attributing too much autonomy to the brain to basing itself on faulty assumptions about our prehistoric past. Epistemological Dimensions of Evolutionary Psychology reframes its discipline for the contemporary era, correcting common misconceptions and mediating (...)
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  31.  44
    Dimensions of election procedures: Analyses and comparisons.Peter C. Fishburn - 1983 - Theory and Decision 15 (4):371-397.
    This paper comments on the history of the search for better election procedures, then discusses dimensions relevant to the evaluation and comparison of ompeting procedures. Its aim is to indicate the variety of factors involved in the search and to suggest an integrative perspective that could aid further research. The dimensions examined include the nomination process, agenda formation, candidate strategy, voter psychology and strategy, ballot forms and methods of aggregation, evaluative aspects of aggregation, incentive compatibility, costs and financing, and institutional (...)
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  32.  8
    Scope, Dimensions, Measurements and Mobilizations.Bernard Ancori - 2019-12-16 - In The Carousel of Time. Hoboken, NJ, USA: Wiley. pp. 81–111.
    Communications and categorizations mark the temporality of the possible sequences of network states, and each event thus produced modifies the space of the network by provoking in individual actors various types of learning that present an extensive and intensive dimension. This chapter examines in detail these types of learning and the mobilizations of the network space involved. Like inter‐individual communication, categorization potentially impacts both dimensions of learning. The chapter first discusses learning from inter‐individual communication, and shows that it is (...)
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  33. Dimensions of mind perception.Heather Gray, Kurt Gray & Daniel Wegner - 2007 - Science 315 (5812):619.
    Participants compared the mental capacities of various human and nonhuman characters via online surveys. Factor analysis revealed two dimensions of mind perception, Experience and Agency. The dimensions predicted different moral judgments but were both related to valuing of mind.
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  34. Dimensions of integration in embedded and extended cognitive systems.Richard Heersmink - 2015 - Phenomenology and the Cognitive Sciences 14 (3):577-598.
    The complementary properties and functions of cognitive artifacts and other external resources are integrated into the human cognitive system to varying degrees. The goal of this paper is to develop some of the tools to conceptualize this complementary integration between agents and artifacts. It does so by proposing a multidimensional framework, including the dimensions of information flow, reliability, durability, trust, procedural transparency, informational transparency, individualization, and transformation. The proposed dimensions are all matters of degree and jointly they constitute a multidimensional (...)
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  35. Eight Dimensions for the Emotions.Tom Cochrane - 2009 - Social Science Information 48 (3):379-420.
    The author proposes a dimensional model of our emotion concepts that is intended to be largely independent of one’s theory of emotions and applicable to the different ways in which emotions are measured. He outlines some conditions for selecting the dimensions based on these motivations and general conceptual grounds. Given these conditions he then advances an 8-dimensional model that is shown to effectively differentiate emotion labels both within and across cultures, as well as more obscure expressive language. The 8 dimensions (...)
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  36.  42
    Dimensions of the Sacred: An Anatomy of the World's Beliefs.Ninian Smart - 1996 - Univ of California Press.
    "Dimensions of the Sacred is arguably one of the most comprehensive and readable accounts of religion that we have had in the past thirty years. Not only does it provide a rich analysis of religious experience, but he also includes much that has been overlooked by other interpreters of the world's religions."—Richard D. Hecht, coauthor of The Sacred Texts of the World.
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  37.  22
    Division rings whose vector spaces are pseudofinite.Lou Den Drievans & Vinicius Cifú Lopes - 2010 - Journal of Symbolic Logic 75 (3):1087-1090.
    Vector spaces over fields are pseudofinite, and this remains true for vector spaces over division rings that are finite-dimensional over their center. We also construct a division ring such that the nontrivial vector spaces over it are not pseudofinite, using Richard Thompson's group F. The idea behind the construction comes from a first-order axiomatization of the class of division rings all whose nontrivial vector spaces are pseudofinite.
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  38. Dimensions of scientific law.Sandra D. Mitchell - 2000 - Philosophy of Science 67 (2):242-265.
    Biological knowledge does not fit the image of science that philosophers have developed. Many argue that biology has no laws. Here I criticize standard normative accounts of law and defend an alternative, pragmatic approach. I argue that a multidimensional conceptual framework should replace the standard dichotomous law/ accident distinction in order to display important differences in the kinds of causal structure found in nature and the corresponding scientific representations of those structures. To this end I explore the dimensions of stability, (...)
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  39. Moral dimensions: permissibility, meaning, blame.Thomas Scanlon - 2008 - Cambridge: Belknap Press of Harvard University Press.
    The illusory appeal of double effect -- The significance of intent -- Means and ends -- Blame.
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  40. In Defence of Dimensions.Caspar Jacobs - forthcoming - British Journal for the Philosophy of Science.
    The distinction between dimensions and units in physics is commonplace. But are dimensions a feature of reality? The most widely-held view is that they are no more than a tool for keeping track of the values of quantities under a change of units. This anti-realist position is supported by an argument from underdetermination: one can assign dimensions to quantities in many different ways, all of which are empirically equivalent. In contrast, I defend a form of dimensional realism, on which some (...)
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  41.  41
    Krull dimension in modal logic.Guram Bezhanishvili, Nick Bezhanishvili, Joel Lucero-Bryan & Jan van Mill - 2017 - Journal of Symbolic Logic 82 (4):1356-1386.
    We develop the theory of Krull dimension forS4-algebras and Heyting algebras. This leads to the concept of modal Krull dimension for topological spaces. We compare modal Krull dimension to other well-known dimension functions, and show that it can detect differences between topological spaces that Krull dimension is unable to detect. We prove that for aT1-space to have a finite modal Krull dimension can be described by an appropriate generalization of the well-known concept of a (...)
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  42. Dimensions of mind.Richard Menary - 2010 - Phenomenology and the Cognitive Sciences 9 (4):561-578.
    In their papers for this issue, Sterelny and Sutton provide a dimensional analysis of some of the ways in which mental and cognitive activities take place in the world. I add two further dimensions, a dimension of manipulation and of transformation. I also discuss the explanatory dimensions that we might use to explain these cases.
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  43. The Dimensions of Consequentialism: Ethics, Equality and Risk.Martin Peterson - 2013 - Cambridge: Cambridge University Press.
    Consequentialism, one of the major theories of normative ethics, maintains that the moral rightness of an act is determined solely by the act's consequences and its alternatives. The traditional form of consequentialism is one-dimensional, in that the rightness of an act is a function of a single moral aspect, such as the sum total of wellbeing it produces. In this book Martin Peterson introduces a new type of consequentialist theory: multidimensional consequentialism. According to this theory, an act's moral rightness depends (...)
  44.  34
    Division rings whose vector spaces are pseudofinite.Vinicius Lopes & Lou van den Dries - 2010 - Journal of Symbolic Logic 75 (3):1087-1090.
    Vector spaces over fields are pseudofinite, and this remains true for vector spaces over division rings that are finite-dimensional over their center. We also construct a division ring such that the nontrivial vector spaces over it are not pseudofinite, using Richard Thompson's group F. The idea behind the construction comes from a first-order axiomatization of the class of division rings all whose nontrivial vector spaces are pseudofinite.
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  45.  22
    (1 other version)Robert Alexy’s Ideal Dimension of Law.Andrea Porciello - 2017 - Archiv für Rechts- und Sozialphilosophie 103 (4):483-493.
    The main purpose Robert Alexy tries to achieve with The argument from Injustice and all the other works he wrote on the same topic is to prove, against legal positivism, that law is a bidimensional concept comprising both a real or institutional dimension and an ideal one. As we know, positivism believes that law is valid for formal or factual reasons that just contingently, this is the inclusive variant, may incorporate moral elements; otherwise Professor Alexy believes that law, the (...)
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  46. Dimensions of Conspiracy: Toward a Unifying Framework for Understanding Conspiracy Theory Belief.Melina Tsapos - manuscript
    Researchers have argued that believing in conspiracy theories is dangerous and harmful, both for the individual and the community. In the philosophical debate, the divide is between the generalists, who argue that conspiracy theories are prima facie problematic, and the particularists, who argue that since conspiracies do occur, we ought to take conspiracy theories seriously, and consider them on merit. Much of the empirical research has focused on correlations between conspiracy belief and personality traits, such as narcissism, illusory pattern perception, (...)
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  47. Cultural Dimensions, Ethical Sensitivity, and Corporate Governance.Alex W. H. Chan & Hoi Yan Cheung - 2012 - Journal of Business Ethics 110 (1):45-59.
    The economic globalization process has integrated different competitive markets and pushes firms in different countries to improve their managerial and operational efficiencies. Given the recent empirical evidence for the benefits to firms and stakeholders of good corporate governance (CG) practice, it is expected that good CG practice would be a common strategy for firms in different countries to meet the increasingly intense competition; however, this is not the case. This study examines the differences in CG practices in firms across different (...)
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  48. Dimensions of observability.Peter Kosso - 1988 - British Journal for the Philosophy of Science 39 (4):449-467.
    The concept of observability of entities in physical science is typically analysed in terms of the nature and significance of a dichotomy between observables and unobservables. In the present work, however, this categorization is resisted and observability is analysed in a descriptive way in terms of the information which one can receive through interaction with objects in the world. The account of interaction and the transfer of information is done using applicable scientific theories. In this way, the question of observability (...)
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  49.  20
    Perceptual dimensions differentiate emotions.Lisa A. Cavanaugh, Deborah J. MacInnis & Allen M. Weiss - 2016 - Cognition and Emotion 30 (8).
    Individuals often describe objects in their world in terms of perceptual dimensions that span a variety of modalities; the visual (e.g., brightness: dark–bright), the auditory (e.g., loudness: quiet–loud), the gustatory (e.g., taste: sour–sweet), the tactile (e.g., hardness: soft vs. hard) and the kinaesthetic (e.g., speed: slow–fast). We ask whether individuals use perceptual dimensions to differentiate emotions from one another. Participants in two studies (one where respondents reported on abstract emotion concepts and a second where they reported on specific emotion episodes) (...)
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  50.  16
    Les dimensions de l'exigence communiste chez Mascolo.Robert Vander Gucht - 1970 - Revue Philosophique De Louvain 68 (98):193-241.
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