Abstract

The present paper is a continuation of [6] and [7]. Thus the content of this paper is the following. At first we establish properties of systems S 2 n and S 2∗ n, where systems S 2 n and S 2∗ n are extensions of Rasiowa-S lupecki’s systems Sn and S ∗ n. Then we shall show that for every cardinal number m there exist a system ST 4 m of propositional calculus and a system SP 4 m of predicate calculus such that the system ST 4 m has exactly m Lindenbaum’s oversystems and the system SP 4 m has exactly m Lindenbaum’s oversystems, where 1 ≤ m ≤ 2 ℵ0.