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Set Theory
Boolean-Valued Models and Independence Proofs
Bell, John L.
Professor of Philosophy, University of Western Ontario
Print publication date: 2005 (this edition)
Published to Oxford Scholarship Online: September 2007
Print ISBN-13: 978-0-19-856852-0
doi:10.1093/acprof:oso/9780198568520.003.0001
0 BOOLEAN AND HEYTING ALGEBRAS: THE ESSENTIALS
John L. Bell
This chapter provides a brief account of the theory of Boolean and Heyting algebras, including the basic representation theorems and their connections with logic.
Keywords:
lattice
,
Boolean algebra
,
Heyting algebra
,
representation theorem
doi:10.1093/acprof:oso/9780198568520.003.0001
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Contents
Full Book Contents
Preface
0 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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