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Titlebook: Axiomatic Set Theory; Gaisi Takeuti,Wilson M. Zaring Textbook 1973 Springer-Verlag New York Inc. 1973 forcing.proof.set theory

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期刊全称Axiomatic Set Theory
影响因子2023Gaisi Takeuti,Wilson M. Zaring
视频video
学科分类Graduate Texts in Mathematics
图书封面Titlebook: Axiomatic Set Theory;  Gaisi Takeuti,Wilson M. Zaring Textbook 1973 Springer-Verlag New York Inc. 1973 forcing.proof.set theory
影响因子This text deals with three basic techniques for constructing models of Zermelo-Fraenkel set theory: relative constructibility, Cohen‘s forcing, and Scott-Solovay‘s method of Boolean valued models. Our main concern will be the development of a unified theory that encompasses these techniques in one comprehensive framework. Consequently we will focus on certain funda­ mental and intrinsic relations between these methods of model construction. Extensive applications will not be treated here. This text is a continuation of our book, "I ntroduction to Axiomatic Set Theory," Springer-Verlag, 1971; indeed the two texts were originally planned as a single volume. The content of this volume is essentially that of a course taught by the first author at the University of Illinois in the spring of 1969. From the first author‘s lectures, a first draft was prepared by Klaus Gloede with the assistance of Donald Pelletier and the second author. This draft was then rcvised by the first author assisted by Hisao Tanaka. The introductory material was prepared by the second author who was also responsible for the general style of exposition throughout the text. We have inc1uded in the introductory mate
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Boolean-Valued Structures,ruth values “truth” and “falsehood” by any complete Boolean algebra B. While some of the basic definitions and theorems can be generalized to the B-valued case almost mechanically the intuitive ideas behind these general notions are more difficult to perceive.
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Boolean-Valued Relative Constructibility,will denote the language of the first-order predicate calculus with predicate constants = and ϵ. In addition L is a first order language that is an extension of L.. In most applications L will have only finitely many constants but it may have infinitely many. M and M’ will be two B-valued structures
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Forcing,hroughout this section, . denotes a standard transitive model of ., . ∈ . is a partial order structure, and . is the corresponding .-complete Boolean algebra of regular open sets of . in the relative sense of .. Further-more we have.Such that ., ., and . are related to each as described in §2. Thus
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Cardinals in V(B),ollary 14.23. However, since this translation requires the existence of elementary subsystems of . and thus cannot be carried out in . we shall try to give direct proofs in .. Corresponding to the fact that every cardinal in .[.], where 〈., .〉 is a setting for forcing and . is .-generic over ., is a
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Axiomatic Set Theory978-1-4684-8751-0Series ISSN 0072-5285 Series E-ISSN 2197-5612
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