| Document Type
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BL
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| Record Number
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974992
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| Doc. No
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b729362
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| Main Entry
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Fraenkel, Abraham Adolf,1891-1965.
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| Title & Author
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Foundations of set theory\ Abraham A. Fraenkel, Yehoshua Bar-Hillel [and] Azriel Levey. With the collaboration of Dirk van Dalen.
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| Edition Statement
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2nd ed.
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| Publication Statement
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Amsterdam :: Elsevier Science,, 1973.
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| Series Statement
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Studies in logic and the foundations of mathematics ;; v. 67
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| Page. NO
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1 online resource (415 p.).
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| ISBN
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0080887058
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: 6611777652
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: 9780080887050
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: 9786611777654
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| Notes
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Description based upon print version of record.
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| Bibliographies/Indexes
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Includes bibliography.
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| Contents
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Front Cover; Foundations of Set Theory; Copyright Page; Contents; Preface; CHAPTER I. THE ANTINOMIES; 1. Historical introduction; 2. Logical antinomies; 3. Semantical antinomies; 4. General remarks; 5. The three crises; CHAPTER II. AXIOMATIC FOUNDATIONS OF SET THEORY; 1. Introduction; 2. Some basic notions, equality and extensionality; 3. Axioms of comprehension and infinity; 4. The axiom of choice; 5. The axiom of foundation; 6. Questions unanswered by the axioms; 7. The role of classes in set theory; CHAPTER III. TYPE-THEORETICAL APPROACHES; 1. The ideal calculus; 2. The theory of types
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4. Mathematics and logic. Logical calculus5. The primordial intuition of integer. Choice sequences and Brouwer's concept of set; 6. Mathematics as trimmed according to the intuitionistic attitude; CHAPTER V. METAMATHEMATICAL AND SEMANTICAL APPROACHES; 1. The Hilbert program; 2. Formal systems, logistic systems, and formalized theories; 3. Interpretations and models; 4. Consistency, completeness, categoricalness, and independence; 5. The Skolem-Löwenheim theorem; Skolem's paradox; 6. Decidability and recursiveness; arithmetization of syntax
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7. The limitative theorems of Gödel, Tarski, Church and their generalizations8. The metamathematics and semantics of set theory; 9. Philosophical remarks; Bibliography; Index of persons; Index of symbols; Subject index
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| Abstract
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Foundations of Set Theory.
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| Subject
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Mathematics-- Philosophy.
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| Subject
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Set theory.
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| Subject
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Mathematics-- Philosophy.
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| Subject
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Set theory.
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| Dewey Classification
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511.3511''.3511/.3
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| LC Classification
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QA248.F753 1973
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| Added Entry
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Bar-Hillel, Yehoshua.
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Levy, Azriel.
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