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On identities and equations in Post algebras. (English) Zbl 1028.03049

The author provides the following contributions to the theory of Post functions and equations: two characterizations of an inequality \(x\leq y\) in terms of the disjunctive components of \(x\) and \(y\), two new descriptions of the relative pseudocomplement \(x\to y\), 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.

MSC:

03G20 Logical aspects of Łukasiewicz and Post algebras
06D25 Post algebras (lattice-theoretic aspects)
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