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math.LO2024
Minimal signatures with undecidability of representability by binary relations
Robin Hirsch, Marcel Jackson, Jaš Šemrl
A semigroup of binary relations (under composition) on a set is \emph{complemented} if it is closed under the taking of complements within . We resolve a 1991 proble…
math.LO2023
Implication Algebras and Implication Semigroups of Binary Relations
Andrew Lewis-Smith Jaš Šemrl
Representable implication algebras are known to be axiomatised by a finite number of equations (making the representation and finite representation problems decidable here). We sho…
math.LO2021
Finite Representation Property for Relation Algebra Reducts
Jaš Šemrl
The decision problem of membership in the Representation Class of Relation Algebras (RRA) for finite structures is undecidable. However, this does not hold for many Relation Algebr…