Non-finite axiomatizability of reducts of algebras of relations

Axiomatizability of Reducts of Algebras of Relations

Complexity of Equations Valid in Algebras of Relations: Part II: Finite Axiomatizations

We study algebras whose elements are relations, and the operations are natural \manipulations" of relations. This area goes back to 140 years ago to works of De Morgan, Peirce, Schrr oder (who expanded the Boolean tradition with extra operators to handle algebras of binary relations). Well known examples of algebras of relations are the varieties RCA n of cylindric algebras of n-ary relations, ...

Complexity of Equations Valid in Algebras of Relations: Part I: Strong Non-Finitizability

We study algebras whose elements are relations, and the operations are natural \manipulations" of relations. This area goes back to 140 years ago to works of De Morgan, Peirce, Schrr oder (who expanded the Boolean tradition with extra operators to handle algebras of binary relations). Well known examples of algebras of relations are the varieties RCA n of cylindric algebras of n-ary relations, ...

On Finite Axiomatizability of Expansions of Cylindric Algebras

We study expansions of (representable) cylindric algebras ( ) ω CA R that are reducts of polyadic equality algebras. The question we adress is: Can we add finitely many substitutions, so that in the expanded language of , ω CA there is a finite set of quantifier free formulas that force representability of the cylindric reduct of algebras satisfying them. A refinement of a known positive soluti...

Finite Axiomatizability of Congruence Rich Varieties

In this paper we introduce the notion of a congruence rich variety of algebras, and investigate which locally finite subvarieties of such a variety are relatively finitely based. We apply the results obtained to investigate the finite axiomatizability of an interesting variety generated by a particular five-element directoid. Roughly speaking, congruence rich varieties are those in which all la...