Subject: Mathematics Book Title: Set Theory
Set Theory
Boolean-Valued Models and Independence Proofs
Bell, John L.,
Professor of Philosophy, University of Western Ontario
Third Edition
Print publication date: 2005
Published to Oxford Scholarship Online: September 2007 Print ISBN-13: 978-0-19-856852-0 doi:10.1093/acprof:oso/9780198568520.001.0001 |
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Abstract:
This is the third edition of a well-known graduate textbook on Boolean-valued models of set theory. The aim of the first and second editions was to provide a systematic and adequately motivated exposition of the theory of Boolean-valued models as developed by Scott and Solovay in the 1960s, deriving along the way the central set theoretic independence proofs of Cohen and others in the particularly elegant form that the Boolean-valued approach enables them to assume. In this edition, the background material has been augmented to include an introduction to Heyting algebras. It includes chapters on Boolean-valued analysis and Heyting-algebra-valued models of intuitionistic set theory.
Keywords: lattice, Boolean algebra, Heyting algebra, Boolean-valued model, continuum hypothesis, ultrailter, axiom of choice, forcing, generic, category Table of Contents
Preface
BOOLEAN AND HEYTING ALGEBRAS: THE ESSENTIALS
1.
BOOLEAN-VALUED MODELS OF SET THEORY: FIRST STEPS
2.
FORCING AND SOME INDEPENDENCE PROOFS
3.
GROUP ACTIONS ON V
AND THE INDEPENDENCE OF THE AXIOM OF CHOICE
4.
GENERIC ULTRAFILTERS AND TRANSITIVE MODELS OF ZFC
5.
CARDINAL COLLAPSING, BOOLEAN ISOMORPHISM, AND APPLICATIONS TO THE THEORY OF BOOLEAN ALGEBRAS
6.
ITERATED BOOLEAN EXTENSIONS, MARTIN'S AXIOM, AND SOUSLIN'S HYPOTHESIS
7.
BOOLEAN-VALUED ANALYSIS
8.
INTUITIONISTIC SET THEORY AND HEYTING-ALGEBRA-VALUED MODELS
Appendix
Bibliography
Index
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doi:10.1093/acprof:oso/9780198568520.001.0001
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