Set Theory and the Continuum Problem
Published on 1. August 1996
Book
Hardback
301 pages
978-0-19-852395-6 (ISBN)
Description
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. This book is intended for graduate students and researchers in mathematical logic.
More details
Language
English
Place of publication
Oxford
United Kingdom
Publishing group
Oxford University Press
Target group
College/higher education
Professional and scholarly
Illustrations
2 line figures, bibliography
ISBN-13
978-0-19-852395-6 (9780198523956)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Classification
Persons
Content
Part I. 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. Part II. Mostowski-Shepherdson Mappings. Reflection principles. Constructible sets. L is well founded first-order universe. Constructability is absolute over L. Constructability and the continuum hypothesis. Part III. 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