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arXiv · 2301.02266

Implication Algebras and Implication Semigroups of Binary Relations

Andrew Lewis-Smith Jaš Šemrl
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Abstract

Representable implication algebras are known to be axiomatised by a finite number of equations (making the representation and finite representation problems decidable here). We show that this also holds in the context of unary (and binary) relations and present a Stone-style representation theorem. We then show that the (finite) representation decision problem is undecidable for implication semigroups, in stark contrast with implication algebras.

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BibTeXRIS

Andrew Lewis-Smith Jaš Šemrl. 2023-01-05. Implication Algebras and Implication Semigroups of Binary Relations. https://arxiv.org/abs/2301.02266

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