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Set Theory: Boolean-Valued Models and Independence Proofs

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

BOOLEAN-VALUED MODELS OF SET THEORY: FIRST STEPS

Chapter:
(p. 16 ) 1 BOOLEAN-VALUED MODELS OF SET THEORY: FIRST STEPS
Source:
Set Theory
Author(s):

John L. Bell

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198568520.003.0002

This chapter presents a brief overview of the concepts from axiomatic set theory, then constructs the Boolean-valued universe V(B) and establishes its basic properties. The idea of a mixture of Boolean-valued sets is introduced and used to prove the Maximum Principle. The truth of the axioms of set theory in V(B) is then established. The chapter concludes with a discussion of ordinals, cardinals, and constructible sets V(B).

Keywords:   mixture, Maximum Principle, ordinal, cardinal, constructible set

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