Abstract
Algebras with certain operations of Tarski relation algebras are studied. Such are called reducts of Tarski relation algebras. We discuss the problems of obtaining an axiomatic description of classes of reducts of Tarski relation algebras with the set of operations {o, ∩}⊂Ω⊂{o, ∩,∪, ø, U} and of providing a characterization of varieties and quasivarieties generated by them.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. Tarski, “On the calculus of relations”,J. Symb. Log.,6, 73–89 (1941).
A. Tarski, “Some methodological results concerning the calculus of relations”,J. Symb. Log.,18, 188–189 (1953).
D. A. Bredikhin, “On relation algebras with general superpositions”,Coll. Math. Soc. János Bolyai,54, 111–124 (1991).
B. M. Schein, “Representation of reducts of Tarski relation algebras”,Coll. Math. Soc. János Bolyai,54, 379–394 (1991).
H. Andréka and D. A. Bredikhin, “The equational theory of union-free algebras of relations”,Alg. Univ.,33, 516–532 (1994).
D. A. Bredikhin and B. M. Schein, “Representations of ordered semigroups and lattices by binary relations”,Coll. Math.,49, 2–12 (1978).
H. Andréka, “Representations of distributive lattice-ordered semigroups with binary relations”,Alg. Univ.,28, 12–25 (1991).
A. I. Mal’tsev,Algebraic Systems [in Russian], Nauka, Moscow (1970).
B. M. Schein, “Relation algebras and function semigroups”,Semigroup Forum,1, 1–62 (1970).
D. A. Bredikhin, “Equational theory of relation algebras with positive operations”,Izv. Vyssh. Uch. Zav., Mat., No. 3, 23–30 (1993).
Additional information
Translated fromAlgebra i Logika, Vol. 37, No. 1, pp. 3–16, January–February, 1998.
Rights and permissions
About this article
Cite this article
Bredikhin, D.A. Reducts of Tarski relation algebras. Algebr Logic 37, 1–8 (1998). https://doi.org/10.1007/BF02684080
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02684080