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Set TheoryBoolean-Valued Models and Independence Proofs$
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John L. Bell

Print publication date: 2005

Print ISBN-13: 9780198568520

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198568520.001.0001

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GENERIC ULTRAFILTERS AND TRANSITIVE MODELS OF ZFC

GENERIC ULTRAFILTERS AND TRANSITIVE MODELS OF ZFC

Chapter:
(p.88) 4 GENERIC ULTRAFILTERS AND TRANSITIVE MODELS OF ZFC
Source:
Set Theory
Author(s):

John L. Bell

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198568520.003.0005

The construction of V(B) is relativized to transitive models of ZFC and shown to give rise to actual models of ZFC, in which various set-theoretic assertions are falsified. Boolean-valued set theory is thereby transformed into a valuable model-theoretic tool. The notion of a generic ultrafilter in a Boolean-valued model is introduced in this chapter and shown to play a key role in the discussion.

Keywords:   transitive model, Boolean-valued set theory, generic ultrafilter, ZFC

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