Studies on Church's calculus

Abstract

An extended version of this abstract will appear in Reports on Mathematical Logic. 1. In Church's calculus we establish classes of equivalent formulas built from only one propositional variable p in order to obtain the theorem on existence exactly one Lindenbaum's extension for Church's system. Moreover, we construct a class of finitely axiomatizable systems between Church's and Grzegorczyk's systems and we consider the problem of structural completeness of Church's calculus reduced to formulas formed from the variable p (Fragment tekstu).