UID:
almahu_9947368112102882
Format:
1 online resource (529 p.)
Edition:
2nd completely rev. ed.
ISBN:
1-283-52581-X
,
9786613838261
,
0-08-095495-2
Series Statement:
Studies in logic and the foundations of mathematics ; v. 86
Uniform Title:
Teoria mnogości.
Content:
Provability, Computability and Reflection
Note:
Translation of Teoria mnogosci.
,
Front Cover; Set Theory: With an Introduction to Descriptive Set Theory; Copyright Page; Preface to the first edition; Preface to the second edition; Contents; CHAPTER I. Algebra of sets; 1. Propositional calculus; 2. Sets and operations on sets; 3. Inclusion, Empty set; 4. Laws of union, intersection, and subtraction; 5. Properties of symmetric difference; 6. The set 1, complement; 7. Constituents; 8. Applications of the algebra of sets to topology; 9. Boolean algebras; 10. Lattices; CHAPTER II. Axioms of set theory. Relations. Functions
,
4. Finite and infinite setsCHAPTER IV. Generalized union, intersection and Cartesian product; 1. Set-valued functions . Generalized union and intersection; 2. Operations on infinite sequences of sets; 3. Families of sets closed under given operations; 4. σ-additive and δ-multiplicative families of sets; 5. Reduction and separation properties; 6. Generalized Cartesian products; 7. Cartesian products of topological spaces; 8. The Tychonoff theorem; 9. Reduced direct products; 10. Infinite operations in lattices and in Boolean algebras
,
11. Extensions of ordered sets to complete lattices 12. Representation theory for distributive lattices; CHAPTER V. Theory of cardinal numbers; 1. Equipollence. Cardinal numbers; 2. Countable sets; 3. The hierarchy of cardinal numbers; 4. The arithmetic of cardinal numbers; 5. Inequalities between cardinal numbers. The Cantor-Bernstein theorem and its generalizations; 6. Properties of the cardinals a and c; 7. The generalized sum of cardinal numbers; 8. The generalized product of cardinal numbers; CHAPTER VI. Linearly ordered sets; 1. Introduction
,
2. Dense, scattered, and continuous sets 3. Order types ω, η, and λ; 4. Arithmetic of order types; 5. Lexicographical ordering; CHAPTER VII. Well-ordered sets; 1. Definitions. Principle of transfinite induction; 2. Ordinal numbers; 3. Transfinite sequences; 4. Definitions by transfinite induction; 5. Ordinal arithmetic; 6. Ordinal exponentiation; 7. Expansions of ordinal numbers for an arbitrary base; 8. The well-ordering theorem; 9. Von Neumann's method of elimination of ordinal numbers; CHAPTER VIII. Alephs and related topics; 1. Ordinal numbers of power a
,
2. The cardinal K(m). Hartogs' aleph
,
English
Additional Edition:
ISBN 0-7204-0470-3
Language:
English
