Boolean-Valued Models of Set Theory

Abstract

A Boolean algebra is a structure which behaves very much like first order propositional logic. In this thesis, we examine the technique of using Boolean algebras to create different models of set theory. This concept was developed by Scott in 1967, and can be applied in relative consistency proofs in set theory. As an example we show how to use a Boolean-valued model of set theory to prove the relative consistency of the negation of the Continuum hypothesis with the axioms of ZFC.