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On Number of Lindenbaum's Oversystems of Propositional and Predicate Calculi
Author(s) -
Stepień Teodor
Publication year - 1985
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19850312103
Subject(s) - propositional calculus , completeness (order theory) , predicate (mathematical logic) , mathematics , ackermann function , calculus (dental) , discrete mathematics , mathematical economics , computer science , philosophy , linguistics , programming language , inverse , medicine , dentistry , mathematical analysis
0. 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 n and S2∗ 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 ST4 m of propositional calculus and a system SP 4 m of predicate calculus such that the system ST4 m has exactly m Lindenbaum’s oversystems and the system SP4 m has exactly m Lindenbaum’s oversystems, where 1 ≤ m ≤ 2א0 .
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