John L. BELL. Set theory: Boolean-valued models and independence proofs. Oxford: Clarendon press, 2005. Oxford logic guides, no. 47. pp. XXII + 191. ISBN 0-19-856852-5, 987-0-19-856852-0 (pbk) [Book Review]

Philosophia Mathematica 14 (3):392-394 (2006)
This is the third edition of a book originally published in the 1970s; it provides a systematic and nicely organized presentation of the elegant method of using Boolean-valued models to prove independence results. Four things are new in the third edition: background material on Heyting algebras, a chapter on ‘Boolean-valued analysis’, one on using Heyting algebras to understand intuitionistic set theory, and an appendix explaining how Boolean and Heyting algebras look from the perspective of category theory. The book presents results from a number of set theorists and includes an insightful and informative foreword by Dana Scott. Bell's presentation is lively and pleasant to read, and the material is given in a nicely cohesive way.One obvious reason to be interested in independence proofs is that they concern the important question, what is the set-theoretic hierarchy like? The proofs in Bell's book cover some of the most basic and fundamental independence results, such as those concerning the size of the continuum, the independence of the Axiom of Choice from ZF, cardinal collapsing, Souslin's hypothesis, and Martin's Axiom.Since Gödel's incompleteness theorem, it has been known that for any serious candidate list of set-theoretic axioms, there will be statements neither provable nor disprovable from those axioms. What is really interesting, however, and what the independence proofs discussed here show, is how many of the most natural questions about sets are not decided by the standard axioms of ZFC, and how …
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1093/philmat/nkl006
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Download options
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 26,702
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles
On an Algebra of Lattice-Valued Logic.Lars Hansen - 2005 - Journal of Symbolic Logic 70 (1):282 - 318.

Monthly downloads

Added to index


Total downloads

8 ( #487,182 of 2,158,458 )

Recent downloads (6 months)

1 ( #354,692 of 2,158,458 )

How can I increase my downloads?

My notes
Sign in to use this feature

There  are no threads in this forum
Nothing in this forum yet.

Other forums