13 research outputs found
Atom structures of cylindric algebras and relation algebras
Accepted versio
Strongly representable atom structures of relation algebras
Accepted versio
Strongly representable atom structures of cylindric algebras
Published versio
Canonical varieties with no canonical axiomatisation
Accepted versio
Non-representable relation algebras from vector spaces
Extending a construction of Andreka, Givant, and Nemeti (2019), we construct some finite vector spaces and use them to build finite non-representable relation algebras. They are simple, measurable, and persistently finite, and they validate arbitrary finite sets of equations that are valid in the variety RRA of representable relation algebras. It follows that there is no finitely axiomatisable class of relation algebras that contains RRA and validates every equation that is both valid in RRA and preserved by completions of relation algebras. Consequently, the variety generated by the completions of representable relation algebras is not finitely axiomatisable. This answers a question of Maddux (2018)
Non-representable relation algebras from vector spaces
Extending a construction of Andreka, Givant, and Nemeti (2019), we construct some finite vector spaces and use them to build finite non-representable relation algebras. They are simple, measurable, and persistently finite, and they validate arbitrary finite sets of equations that are valid in the variety RRA of representable relation algebras. It follows that there is no finitely axiomatisable class of relation algebras that contains RRA and validates every equation that is both valid in RRA and preserved by completions of relation algebras. Consequently, the variety generated by the completions of representable relation algebras is not finitely axiomatisable. This answers a question of Maddux (2018)
Representability is not decidable for finite relation algebras
Published versio
Relation algebras with n-dimensional relational bases
Accepted versio
Omitting Types in Fragments and Extensions of First Order Logic
Fix . Let denote first order logic restricted to the first n variables. Using the machinery of algebraic logic, positive and negative results on omitting types are obtained for and for infinitary variants and extensions of