A new proof of structural completeness Łukasiewicz's logics

Abstract

The problem of structural completeness of the finite-valued Lukasiewicz's sentential calculi was investigated and solved in [4], [7], [6]. The present paper contains a new proof of all these results. I. Let (S; F1,...,Fn) be a propositional language. A matrix M = (|M |, |M |*; f1,...,fn) of this language is embeddable in a matrix N = (|N|, |N|*; gi,..., gn) (M C N) iff there exists a monomorphism h : M M N. The symbol N xM stands for the product of matrices and the structural consequence generated by M (cf. [1]) is denoted by M (Fragment tekstu).