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IMCS/Publications/BASM/Issues/BASM n.2 (33), 2000/

On identities and equations in Post algebras. (English)

Authors: Rudeanu S.

Abstract

In the last thirty years several papers have dealt with the theory of Post functions and equations. The present paper provides the following contributions to this topic: two characterizations of an inequality $x \le y$ in terms of the disjunctive components of $x$ and $y$, two new descriptions of the relative pseudocomplement $x \rightarrow\ y$, an intrinsic description of the range of a Post function and the characterization of those functions for which the range is an interval, a characterization of Post equations with unique solutions, as well as several remarks on reproductive solutions of Post equations. These results are generalizations of the corresponding properties for Boolean functions and equations.

University of Bucharest, Faculty of Mathematics
Str. Academiei 14, 70109 Bucharest, Romania
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