UID:
almahu_9949697970102882
Format:
1 online resource (415 p.)
Edition:
2d rev. ed.
ISBN:
1-281-77765-X
,
9786611777654
,
0-08-088705-8
Series Statement:
Studies in logic and the foundations of mathematics ; v. 67
Content:
Foundations of Set Theory
Note:
Description based upon print version of record.
,
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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3. Quine's new foundations4. Quine's mathematical logic; 5. The hierarchy of languages and the ramified class calculus; 6. Wang's system Σ; 7. Lorenzen's operationist system; 8. The logicistic thesis; 9. Types, categories, and sorts; 10. Impredicative concept formation; 11. Set theories based upon non-standard logics; CHAPTER IV. INTUITIONISTIC CONCEPTIONS OF MATHEMATICS; 1. Historical introduction. The abyss between discreteness and continuity; 2. The constructive character of mathematics. Mathematics and language; 3. The principle of the excluded middle
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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
,
English
Additional Edition:
ISBN 0-7204-2270-1
Language:
English
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