Introduction to Modern Set Theory

by Judith Roitman

Overview

Introduction to Modern Set Theory is designed for a one-semester course in set theory at the advanced undergraduate or beginning graduate level. Three features are the full integration into the text of the study of models of set theory, the use of illustrative examples both in the text and in the exercises, and the integration of consistency results and large cardinals into the text early on. This book is aimed at two audiences: students who are interested in studying set theory for its own sake, and students in other areas who may be curious about applications of set theory to their field. In particular, great care is taken to develop the intuitions that lie behind modern, as well as classical, set theory, and to connect set theory with the rest of mathematics.

Product Details

ISBN-13:	9780989897518
Publisher:	Orthogonal Publishing L3C
Publication date:	12/01/2013
Edition description:	3rd ed.
Pages:	220
Sales rank:	1,184,202
Product dimensions:	6.14(w) x 9.21(h) x 0.46(d)

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.