The monotone class theorem in infinitary logic

Abstract:

A monotone formula in the infinitary logic ${L_{{\omega _1}\omega }}$ is a formula which is built up from finite formulas using only quantifiers and monotone countable conjunctions and disjunctions. The monotone class theorem from measure theory is used to show that every formula of ${L_{{\omega _1}\omega }}$ is logically equivalent to a monotone formula (the monotone normal form theorem). The proof is effectivized in order to obtain similar normal form theorems for admissible logics ${L_A}$.