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Other titles in the Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts series:

Introduction to Modern Set Theory (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts)

Introduction to Modern Set Theory (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts) Cover

 

Synopses & Reviews

Publisher Comments:

This is modern set theory from the ground up--from partial orderings and well-ordered sets to models, infinite cobinatorics and large cardinals. The approach is unique, providing rigorous treatment of basic set-theoretic methods, while integrating advanced material such as independence results, throughout. The presentation incorporates much interesting historical material and no background in mathematical logic is assumed. Treatment is self-contained, featuring theorem proofs supported by diagrams, examples and exercises. Includes applications of set theory to other branches of mathematics.

Table of Contents

Some Mathematical Preliminaries.

Partially Ordered Sets.

Some Facts About Partially Ordered Sets.

Equivalence Relations.

Well-Ordered Sets.

Mathematical Induction.

Models.

THE AXIOMS, PART I. The Language, Some Finite Operations, and Extensionality.

Pairs.

Cartesian Products.

Union, Intersection, and Separation.

Filters and Ideas.

The Natural Numbers.

Two Nonconstructive Axioms: Infinity and Power Set.

A Digression on the Power Set Axiom.

Replacement.

REGULARITY AND CHOICE.

Transitive Sets.

A First Look at Ordinals.

Regularity.

A World About Classes.

The Axiom of Choice.

Four Forms of the Axiom of Choice.

Models of Regularity and Choice.

THE FOUNDATION OF MATHEMATICS.

INFINITE NUMBERS.

Cardinality.

Ordinal Arithmetic.

Cardinal Arithmetic.

Cofinality.

Infinite Operations and More Exponentiation.

Counting.

TWO MODELS OF SET THEORY.

A Set Model for ZFC.

The Constructible Universe.

INFINITE COMBINATORICS.

Partition Calculus.

Trees.

Measurable Cardinals.

CH.

Martin's Axiom.

Stationary Sets.

Bibliography.

Index.

Product Details

ISBN:
9780471635192
Author:
Roitman, Judith
Publisher:
Wiley-Interscience
Location:
New York :
Subject:
Set Theory
Subject:
Logic & Foundations
Copyright:
Edition Description:
Bibliography: p. 147-149.
Series:
Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts
Series Volume:
8
Publication Date:
January 1990
Binding:
Hardback
Grade Level:
Professional and scholarly
Language:
English
Illustrations:
Yes
Pages:
176
Dimensions:
242 x 161 x 16 mm 15.2 oz

Related Subjects

Humanities » Philosophy » Logic
Science and Mathematics » Chemistry » Physical Chemistry
Science and Mathematics » Mathematics » Set Theory

Introduction to Modern Set Theory (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts)
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Product details 176 pages Wiley-Interscience - English 9780471635192 Reviews:
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