Projective Logics and Projective Boolean Algebras ( )

Abstract

Publisher Summary This chapter focuses on the projective logics, projective Boolean algebras, and the study of the analytic sets or projective sets and presents the generalization of this approach to all levels of the projective hierarchy. The chapter discusses various preliminaries, the language of projective logics, axioms, rules of inference, the consistency property, Model Existence Theorem, The Completeness Theorem, n -projective Boolean algebras (which is the generalizations of the Suslin algebras), basic results of Boolean algebras, free n- projective boolean algebras, axioms of propositional logic, a representation theorem for free n p-Boolean algebras, and other theorems. The representation theorem for free projective Boolean algebras provides with a bridge from logic to set theory, but so far nothing was specifically shown so as to give a relationship between the projective field of sets and the projective sets of Lusin and Sierpinski.