Set theory

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Set theory / András Hajnal, Peter Hamburger ; translated by Attila Máté

資料種別:

図書

出版情報:

Cambridge : Cambridge University Press, 1999

形態:

viii, 316 p. ; 23 cm

シリーズ名:

London Mathematical Society student texts ; 48 <BA00194352>

著者名:

ISBN:

9780521593441 [0521593441] (: hbk)
9780521596671 [052159667X] (: pbk)

書誌ID:

BA43832905

子書誌情報

フルテキスト

所蔵情報

他の版・巻

書誌詳細

その他の標題:

Halmazeimélet

注記:

Includes bibliographical references (p. [295]-296) and indexes
Oribinally published in Hungarian as Halmazeimélet

主題:

Set theory

言語:

英語

目次情報:

Preface

Introduction to set theory / Part I.：

Introduction

Notation, conventions / 1.：

Definition of equivalence. The concept of cardinality. The Axiom of Choice / 2.：

Countable cardinal, continuum cardinal / 3.：

Comparison of cardinals / 4.：

Operations with sets and cardinals / 5.：

Examples / 6.：

Ordered sets. Order types. Ordinals / 7.：

Properties of wellordered sets. Good sets. The ordinal operation / 8.：

Transfinite induction and recursion. Some consequences of the Axiom of Choice, the Wellordering Theorem / 9.：

Definition of the cardinality operation. Properties of cardinalities. The cofinality operation / 10.：

Properties of the power operation / 11.：

Hints for solving problems marked with * in Part I

An axiomatic development of set theory / Appendix：

The Zermelo-Fraenkel axiom system of set theory / A1.：

Definition of concepts; extension of the language / A2.：

A sketch of the development. Metatheorems / A3.：

A sketch of the development. Definitions of simple operations and properties (continued) / A4.：

A sketch of the development. Basic theorems, the introduction of [omega] and R (continued) / A5.：

The ZFC axiom system. A weakening of the Axiom of Choice. Remarks on the theorems of Sections 2-7 / A6.：

The role of the Axiom of Regularity / A7.：

Proofs of relative consistency. The method of interpretation / A8.：

Proofs of relative consistency. The method of models / A9.：

Topics in combinatorial set theory / Part II.：

Stationary sets / 12.：

[Delta]-systems / 13.：

Ramsey's Theorem and its generalizations. Partition calculus / 14.：

Inaccessible cardinals. Mahlo cardinals / 15.：

Measurable cardinals / 16.：

Real-valued measurable cardinals, saturated ideals / 17.：

Weakly compact and Ramsey cardinals / 18.：

Set mappings / 19.：

The square-bracket symbol. Strengthenings of the Ramsey counterexamples / 20.：

Properties of the power operation. Results on the singular cardinal problem / 21.：

Powers of singular cardinals. Shelah's Theorem / 22.：

Hints for solving problems of Part II

Bibliography

List of symbols

Name index

Subject index

Preface

Introduction to set theory / Part I.：

Introduction

Notation, conventions / 1.：

Definition of equivalence. The concept of cardinality. The Axiom of Choice / 2.：

Countable cardinal, continuum cardinal / 3.：

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