Boolean Algebras and Logic

TL;DR

This paper explores Boolean algebras, their properties, and their connections to logic and set theory, culminating in a proof of the completeness theorem for propositional logic via Stone's representation theorem.

Contribution

It provides a detailed study of Boolean algebras and offers a novel proof of the completeness theorem using Stone's representation theorem.

Findings

Proves Stone's representation theorem for Boolean algebras

Establishes connections between Boolean algebras, logic, and set theory

Provides a proof of the completeness theorem in propositional logic

Abstract

In this article we investigate the notion and basic properties of Boolean algebras and prove the Stone's representation theorem. The relations of Boolean algebras to logic and to set theory will be studied and, in particular, a neat proof of completeness theorem in propositional logic will be given using Stone's theorem from Boolean algebra.