(Ebook) Set Theory Boolean Valued Models and Independence Proofs 3rd Edition by J L Bell ISBN 0198531680 9780198531685

(Ebook) Set Theory Boolean Valued Models and Independence Proofs 3rd Edition by J L Bell ISBN 0198531680 9780198531685

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Product details:

ISBN 10: 0198531680 
ISBN 13: 9780198531685
Author: J L Bell

This third edition, now available in paperback, is a follow up to the author's classic Boolean-Valued Models and Independence Proofs in Set Theory,. It provides an exposition of some of the most important results in set theory obtained in the 20th century: the independence of the continuum hypothesis and the axiom of choice. Aimed at graduate students and researchers in mathematics, mathematical logic, philosophy, and computer science, the third edition has been extensively updated with expanded introductory material, new chapters, and a new appendix on category theory. It covers recent developments in the field and contains numerous exercises, along with updated and increased coverage of the background material. This new paperback edition includes additional corrections and, for the first time, will make this landmark text accessible to students in logic and set theory.

(Ebook) Set Theory Boolean Valued Models and Independence Proofs 3rd Table of contents:

1 Boolean-valued Models of Set Theory; First Steps
Basic set theory
Construction of the model
Subalgebras and their models
Mixtures and the Maximum Principle
The truth of the axioms of set theory in
Ordinals and constructible sets in
Cardinals in VB
2 Forcing and Some Independence Proofs
The forcing relation
Independence of the axiom of constructibility and the continuum hypothesis
Problems
3 Group Actions on ν(β) and the Independence of the Axiom of Choice
Group actions on V B
The independence of the existence of definable well-orderings of P ω
Problems
The independence of the axiom of choice
4 Generic Ultrafilters and Transitive Models of ZFC
Problems
5 Cardinal Collapsing, Boolean Isomorphism, and Applications to the Theory of Boolean Algebras
Cardinal collapsing
Boolean isomorphism and infinitary equivalence
Applications to the theory of Boolean algebras
6 Iterated Boolean Extensions, Martin’s Axiom, and Sousliirs Hypothesis
Souslin’s hypothesis
The independence of SH
Martin’s axiom
Iterated Boolean extensions
Further results on Boolean algebras
The relative consistency of SH
Problems
7 Boolean-valued Analysis
Boolean-valued models built from measure algebras
Boolean-valued models built from algebras of projections
8 Intuitionistic Set Theory and Heyting-Algebra-Valued Models
Intuitionistic Zerrnelo set theory
Intuitionistic Zermelo-Fraenkel set theory
Heyting-algebra-vaiued models
Forcing in Heyting-algebra-valued models and independence in IZF
Appendix: Boolean and Heyting Algebra-Valued Models as Categories
Categories and functors
Toposes
Boolean and Heyting algebra-valued models as toposes

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Tags: J L Bell, Boolean, Valued