Abraham A. Fraenkel, Yehoshua Bar-Hillel [and] Azriel Levey. With the collaboration of Dirk van Dalen.
2nd ed.
Amsterdam :
Elsevier Science,
1973.
1 online resource (415 p.).
Studies in logic and the foundations of mathematics ;
v. 67
Description based upon print version of record.
Includes bibliography.
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
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
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