Extension by Conservation. Sikorski's Theorem

Abstract

Constructive meaning is given to the assertion that every finite Boolean algebra is an injective object in the category of distributive lattices. To this end, we employ Scott's notion of entailment relation, in which context we describe Sikorski's extension theorem for finite Boolean algebras and turn it into a syntactical conservation result. As a by-product, we can facilitate proofs of several related classical principles.