Results for 'Boolean valued analysis'

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  1.  15
    On a Duality Between Boolean Valued Analysis and Topological Reduction Theory.Hirokazu Nishimura - 1993 - Mathematical Logic Quarterly 39 (1):23-32.
    By creating an unbounded topological reduction theory for complex Hilbert spaces over Stonean spaces, we can give a category-theoretic duality between Boolean valued analysis and topological reduction theory for complex Hilbert spaces. MSC: 03C90, 03E40, 06E15, 46M99.
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  2.  29
    Some Connections Between Boolean Valued Analysis and Topological Reduction Theory for C*-Algebras.Hirokazu Nishimura - 1990 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 36 (5):471-479.
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  3.  8
    Some Connections Between Boolean Valued Analysis and Topological Reduction Theory for C*‐Algebras.Hirokazu Nishimura - 1990 - Mathematical Logic Quarterly 36 (5):471-479.
  4.  23
    Boolean Valued and Stone Algebra Valued Measure Theories.Hirokazu Nishimura - 1994 - Mathematical Logic Quarterly 40 (1):69-75.
    In conventional generalization of the main results of classical measure theory to Stone algebra valued measures, the values that measures and functions can take are Booleanized, while the classical notion of a σ-field is retained. The main purpose of this paper is to show by abundace of illustrations that if we agree to Booleanize the notion of a σ-field as well, then all the glorious legacy of classical measure theory is preserved completely.
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  5.  29
    John L. BELL. Set Theory: Boolean-Valued Models and Independence Proofs. Oxford: Clarendon Press, 2005. Oxford Logic Guides, No. 47. Pp. XXII + 191. ISBN 0-19-856852-5, 987-0-19-856852-0 (Pbk). [REVIEW]Patricia Marino - 2006 - Philosophia Mathematica 14 (3):392-394.
    This is the third edition of a book originally published in the 1970s; it provides a systematic and nicely organized presentation of the elegant method of using Boolean-valued models to prove independence results. Four things are new in the third edition: background material on Heyting algebras, a chapter on ‘Boolean-valued analysis’, one on using Heyting algebras to understand intuitionistic set theory, and an appendix explaining how Boolean and Heyting algebras look from the perspective of (...)
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  6.  31
    A Boolean Transfer Principle From L*‐Algebras to AL*‐Algebras.Hirokazu Nishimura - 1993 - Mathematical Logic Quarterly 39 (1):241-250.
    Just as Kaplansky [4] has introduced the notion of an AW*-module as a generalization of a complex Hilbert space, we introduce the notion of an AL*-algebra, which is a generalization of that of an L*-algebra invented by Schue [9, 10]. By using Boolean valued methods developed by Ozawa [6–8], Takeuti [11–13] and others, we establish its basic properties including a fundamental structure theorem. This paper should be regarded as a continuation or our previous paper [5], the familiarity with (...)
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  7.  20
    Hard and Soft Preparation Sets in Boolean Games.Paul Harrenstein, Paolo Turrini & Michael Wooldridge - 2016 - Studia Logica 104 (4):813-847.
    A fundamental problem in game theory is the possibility of reaching equilibrium outcomes with undesirable properties, e.g., inefficiency. The economics literature abounds with models that attempt to modify games in order to avoid such undesirable properties, for example through the use of subsidies and taxation, or by allowing players to undergo a bargaining phase before their decision. In this paper, we consider the effect of such transformations in Boolean games with costs, where players control propositional variables that they can (...)
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  8.  10
    Forcing in Nonstandard Analysis.Masanao Ozawa - 1994 - Annals of Pure and Applied Logic 68 (3):263-297.
    A nonstandard universe is constructed from a superstructure in a Boolean-valued model of set theory. This provides a new framework of nonstandard analysis with which methods of forcing are incorporated naturally. Various new principles in this framework are provided together with the following applications: An example of an 1-saturated Boolean ultrapower of the real number field which is not Scott complete is constructed. Infinitesimal analysis based on the generic extension of the hyperreal numbers is provided, (...)
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  9.  45
    Boolean-Valued Models and Independence Proofs in Set Theory.J. L. Bell & Dana Scott - 1981 - Journal of Symbolic Logic 46 (1):165-165.
  10.  30
    Boolean-Valued Second-Order Logic.Daisuke Ikegami & Jouko Väänänen - 2015 - Notre Dame Journal of Formal Logic 56 (1):167-190.
    In so-called full second-order logic, the second-order variables range over all subsets and relations of the domain in question. In so-called Henkin second-order logic, every model is endowed with a set of subsets and relations which will serve as the range of the second-order variables. In our Boolean-valued second-order logic, the second-order variables range over all Boolean-valued subsets and relations on the domain. We show that under large cardinal assumptions Boolean-valued second-order logic is more (...)
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  11.  8
    Boolean-Valued Models and Independence Proofs in Set Theory.J. L. Bell & Dana Scott - 1986 - Journal of Symbolic Logic 51 (4):1076-1077.
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  12.  9
    Set Theory: Boolean-Valued Models and Independence Proofs.John L. Bell - 2011 - Oxford University Press.
    This third edition, now available in paperback, is a follow up to the author's classic Boolean-Valued Models and Independence Proofs in Set Theory. It provides an exposition of some of the most important results in set theory obtained in the 20th century: the independence of the continuum hypothesis and the axiom of choice.
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  13.  36
    On Paraconsistent Weak Kleene Logic: Axiomatisation and Algebraic Analysis.Stefano Bonzio, José Gil-Férez, Francesco Paoli & Luisa Peruzzi - 2017 - Studia Logica 105 (2):253-297.
    Paraconsistent Weak Kleene logic is the 3-valued logic with two designated values defined through the weak Kleene tables. This paper is a first attempt to investigate PWK within the perspective and methods of abstract algebraic logic. We give a Hilbert-style system for PWK and prove a normal form theorem. We examine some algebraic structures for PWK, called involutive bisemilattices, showing that they are distributive as bisemilattices and that they form a variety, \, generated by the 3-element algebra WK; we (...)
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  14.  31
    Boolean Valued Lie Algebras.Hirokazu Nishimura - 1991 - Journal of Symbolic Logic 56 (2):731-741.
    In this paper we study a certain class of Lie algebras over commutative von Neumann algebras satisfying a certain finiteness condition. By using Boolean valued methods developed by Takeuti [8]-[11], we will establish the basic structure and representation theorems.
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  15.  57
    Boolean-Valued Set Theory and Forcing.Richard Mansfield & John Dawson - 1976 - Synthese 33 (2-4):223 - 252.
  16.  2
    Cost-Value Analysis in Health Care: Making Sense Out of Qalys.Erik Nord - 1999 - Cambridge University Press.
    This book is a comprehensive account of what it means to try to quantify health in distributing resources for health care. It examines the concept of QALYs which supposedly makes it more accurate to talk about life in terms of both quality and quantity of years lived when referring to health care policy. It offers an elegant new approach to comparing the costs and benefits of medical interventions. Cost-Utility Analysis is a method designed by economists to aid decision makers (...)
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  17.  6
    Boolean Valued Models and Generalized Quantifiers.Jouko Väänänen - 1980 - Annals of Mathematical Logic 18 (3):193-225.
  18. A Boolean-Valued Version of Gupta's Semantics.Marie La Palme Reyes & Gonzalo E. Reyes - 1989 - Logique Et Analyse 32 (128):247-265.
     
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  19.  28
    Pseudo-Boolean Valued Prolog.Melvin Fitting - 1988 - Studia Logica 47 (2):85-91.
    A generalization of conventional Horn clause logic programming is proposed in which the space of truth values is a pseudo-Boolean or Heyting algebra, whose members may be thought of as evidences for propositions. A minimal model and an operational semantics is presented, and their equivalence is proved, thus generalizing the classic work of Van Emden and Kowalski.
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  20. Cost-Value Analysis in Health Care: Making Sense Out of QALYs.Erik Nord - 2001 - Philosophical Quarterly 51 (202):132-133.
    This book is a comprehensive account of what it means to try to quantify health in distributing resources for health care. It examines the concept of QALYs which supposedly makes it more accurate to talk about life in terms of both quality and quantity of years lived when referring to health care policy. It offers an elegant new approach to comparing the costs and benefits of medical interventions. Cost-Utility Analysis is a method designed by economists to aid decision makers (...)
     
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  21.  7
    BooleanValued Models and Independence Proofs in Set Theory.Mary Tiles - 1979 - Philosophical Books 20 (3):122-124.
  22.  35
    Boolean Valued Dedekind Domains.Hirokazu Nishimura - 1991 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 37 (5-6):65-76.
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  23.  36
    Boolean-Valued Models of Set Theory with Automorphisms.E. G. Hernandez - 1986 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 32 (7-9):117-130.
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  24.  28
    Some Boolean Valued Commutative Algebra.Hirokazu Nishimura - 1991 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 37 (23-24):367-384.
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  25.  12
    Some Boolean Valued Commutative Algebra.Hirokazu Nishimura - 1991 - Mathematical Logic Quarterly 37 (23‐24):367-384.
  26.  14
    BooleanValued Models of Set Theory with Automorphisms.E. G. Hernandez - 1986 - Mathematical Logic Quarterly 32 (7‐9):117-130.
  27.  12
    Boolean Valued Dedekind Domains.Hirokazu Nishimura - 1991 - Mathematical Logic Quarterly 37 (5‐6):65-76.
  28.  4
    Commutative Regular Rings and Boolean-Valued Fields.Kay Smith - 1984 - Journal of Symbolic Logic 49 (1):281-297.
    In this paper we present an equivalence between the category of commutative regular rings and the category of Boolean-valued fields, i.e., Boolean-valued sets for which the field axioms are true. The author used this equivalence in [12] to develop a Galois theory for commutative regular rings. Here we apply the equivalence to give an alternative construction of an algebraic closure for any commutative regular ring.Boolean-valued sets were developed in 1965 by Scott and Solovay [10] (...)
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  29. Set Theory : Boolean-Valued Models and Independence Proofs: Boolean-Valued Models and Independence Proofs.John L. Bell - 2005 - Oxford University Press UK.
    This monograph is a follow up to the author's classic text Boolean-Valued Models and Independence Proofs in Set Theory, providing an exposition of some of the most important results in set theory obtained in the 20th century--the independence of the continuum hypothesis and the axiom of choice. Aimed at research students and academics in mathematics, mathematical logic, philosophy, and computer science, the text has been extensively updated with expanded introductory material, new chapters, and a new appendix on category (...)
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  30.  19
    Eastern Model‐Theory for BooleanValued Theories.George Georgescu & Iana Voiculescu - 1985 - Mathematical Logic Quarterly 31 (1‐6):79-88.
  31.  19
    Sheaves and Boolean Valued Model Theory.George Loullis - 1979 - Journal of Symbolic Logic 44 (2):153-183.
  32.  10
    Simplified Independence Proofs. Boolean Valued Models of Set Theory.J. Barkley Rosser - 1974 - Journal of Symbolic Logic 39 (2):328-329.
  33.  31
    Can Bayesian Agents Always Be Rational? A Principled Analysis of Consistency of an Abstract Principal Principle.Miklós Rédei & Zalán Gyenis - unknown
    The paper takes thePrincipal Principle to be a norm demanding that subjective degrees of belief of a Bayesian agent be equal to the objective probabilities once the agent has conditionalized his subjective degrees of beliefs on the values of the objective probabilities, where the objective probabilities can be not only chances but any other quantities determined objectively. Weak and strong consistency of the Abstract Principal Principle are defined in terms of classical probability measure spaces. It is proved that the Abstract (...)
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  34.  72
    On Bohr's Response to EPR: A Quantum Logical Analysis[REVIEW]Jeffrey Bub - 1989 - Foundations of Physics 19 (7):793-805.
    Bohr's complementarity interpretation is represented as the relativization of the quantum mechanical description of a system to the maximal Boolean subalgebra (in the non-Boolean logical structure of the system) selected by a classically described experimental arrangement. Only propositions in this subalgebra have determinate truth values. The concept of a minimal revision of a Boolean subalgebra by a measurement is defined, and it is shown that the nonmaximal measurement of spin on one subsystem in the spin version of (...)
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  35.  27
    Eastern Model-Theory for Boolean-Valued Theories.George Georgescu & Iana Voiculescu - 1985 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 31 (1-6):79-88.
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  36.  21
    Review: J. L. Bell, Boolean-Valued Models and Independence Proofs in Set Theory; Dana Scott, Foreword. [REVIEW]Thomas Jech - 1981 - Journal of Symbolic Logic 46 (1):165-165.
  37.  24
    Cost-Value Analysis in Health Care: Making Sense Out of QALYs: Eric Nord, Cambridge, Cambridge University Press, 1999, 175 Pages, Pound35 (Hb) Pound11.95 (Pb). [REVIEW]J. McMillan - 2001 - Journal of Medical Ethics 27 (2):139-139.
  38.  11
    Bell J. L.. Boolean-Valued Models and Independence Proofs in Set Theory. Oxford Logic Guides. Clarendon Press, Oxford 1977, Xviii + 126 Pp. [REVIEW]Thomas Jech - 1981 - Journal of Symbolic Logic 46 (1):165-165.
  39.  28
    Foundations of Boolean Valued Algebraic Geometry.Hirokazu Nishimura - 1991 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 37 (26-30):421-438.
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  40.  6
    Review: J. L. Bell, Boolean-Valued Models and Independence Proofs in Set Theory; Dana Scott, Foreword. [REVIEW]James E. Baumgartner - 1986 - Journal of Symbolic Logic 51 (4):1076-1077.
  41.  3
    Bell J. L.. Boolean-Valued Models and Independence Proofs in Set Theory. Second Edition of XLVI 165. Oxford Logic Guides, No. 12. Clarendon Press, Oxford University Press, Oxford and New York 1985, Xx + 165 Pp.Scott Dana. Foreword. A Revised Reprint of XLVI 165. Therein, Pp. Vii–Xiii. [REVIEW]James E. Baumgartner - 1986 - Journal of Symbolic Logic 51 (4):1076-1077.
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  42.  22
    Foundations of Boolean Valued Algebraic Geometry.Hirokazu Nishimura - 1991 - Mathematical Logic Quarterly 37 (26‐30):421-438.
  43. Mathematical Quantum Theory I: Random Ultrafilters as Hidden Variables.William Boos - 1996 - Synthese 107 (1):83 - 143.
    The basic purpose of this essay, the first of an intended pair, is to interpret standard von Neumann quantum theory in a framework of iterated measure algebraic truth for mathematical (and thus mathematical-physical) assertions — a framework, that is, in which the truth-values for such assertions are elements of iterated boolean measure-algebras (cf. Sections 2.2.9, 5.2.1–5.2.6 and 5.3 below).The essay itself employs constructions of Takeuti's boolean-valued analysis (whose origins lay in work of Scott, Solovay, Krauss and (...)
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  44. Three-Valued Analysis of Precise, Vague, and Presupposing Quantifiers'.Ulrich Blau - 1983 - In Thomas T. Ballmer & Manfred Pinkal (eds.), Approaching Vagueness. Elsevier. pp. 79--129.
     
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  45.  21
    Cost-Value Analysis in Health Care: Making Sense Out of QALYs, Erik Nord. [REVIEW]Daniel M. Hausman - 2000 - Economics and Philosophy 16 (2):333-378.
  46. Cost-Value Analysis in Health Care by Erik Nord.John Mckie - unknown
     
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  47. Two Applications of Logic to Mathematics.Gaisi Takeuti - 1955 - Princeton University Press.
    Using set theory in the first part of his book, and proof theory in the second, Gaisi Takeuti gives us two examples of how mathematical logic can be used to obtain results previously derived in less elegant fashion by other mathematical techniques, especially analysis. In Part One, he applies Scott- Solovay's Boolean-valued models of set theory to analysis by means of complete Boolean algebras of projections. In Part Two, he develops classical analysis including complex (...)
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  48.  45
    Towards Cost-Value Analysis in Health Care?Erik Nord - 1999 - Health Care Analysis 7 (2):167-175.
    By describing societal value judgements in health care in numerical terms one may in theory increase the precision of guidelines for priority setting and allow decision makers to judge more accurately the degree to which different health care programs provide societal value for money. However, valuing health programs in terms of QALYs disregards salient societal concerns for fairness in resource allocation. A different kind of numerical valuation of medical interventions, that incorporates concerns for fairness, is described. The usefulness to decision (...)
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  49.  26
    J. Barkley Rosser. Simplified Independence Proofs. Boolean Valued Models of Set Theory. Pure and Applied Mathematics, No. 31. Academic Press, New York and London 1969, Xv + 217 Pp. [REVIEW]Aleksander Rutkowski - 1974 - Journal of Symbolic Logic 39 (2):328-329.
  50. God as the Supreme Value: Analysis and Interpretation of the Idea of God From the Standpoint of Value.Leela D. Gole - 1974 - University of Poona.
     
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