Set Theory and the Continuum Problem

by Smullyan, Raymond M.; Fitting, Melvin

• ISBN13: 9780198523956
• ISBN10: 0198523955
• Format: Hardcover
• Copyright: 1996-11-14
• Publisher: Oxford University Press

Summary

Set Theory and the Continuum Problem is a novel introduction to set theory, including axiomatic development, consistency, and independence results. It is self-contained and covers all the set theory that a mathematician should know. Part I introduces set theory, including basic axioms, development of the natural number system, Zorn's Lemma and other maximal principles. Part II proves the consistency of the continuum hypothesis and the axiom of choice, with material on collapsing mappings, model-theoretic results, and constructible sets. Part III presents a version of Cohen's proofs of the independence of the continuum hypothesis and the axiom of choice. It also presents, for the first time in a textbook, the double induction and superinduction principles, and Cowen's theorem. The book will interest students and researchers in logic and set theory.

Table of Contents

General background

Some basics of class-set theory

The natural number

Superinduction, well ordering and choice

Ordinal numbers

Order isomorphism and transfinite recursion

Rank

Foundation, e-induction, and rank

Cardinals

Mostowski-Shepherdson Mappings

Reflection principles

Constructible sets

L is well founded first-order universe

Constructability is absolute over L

Constructability and the continuum hypothesis

Forcing, the very idea

The construction of S4 models and ZF

The axion of constructability is independent

Independence of the continuum hypothesis

Independence of the axiom of choice

Constructing classical models

Forcing background

References

Subject Index

Notation Index

Table of Contents provided by Publisher. All Rights Reserved.