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International Conference on Modern Algebra in conjunction with the 17th annual Shanks Lectures
May 21-24, 2002
Vanderbilt University
Nashville, TN, USA

Organizers
Jonathan Farley, Ralph Freese, Matthew Gould, Peter Jipsen, George McNulty, Miklos Maroti, Alexander Ol'shanskii, Steven Tschantz, Constantine Tsinakis, Matthew Valeriote

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Axiomatizability of algebras of binary relations
by
Szabolcs Mikulas
Birkbeck College, University of London

Tarski's class of representable relation algebras, RRA, is a non-finitely axiomatizable variety [Monk].

The aim of this talk to investigate finite axiomatizability of algebras of binary relations with smaller expressive power than that of RRA.

In particular, we focus on algebras with a semilattice structure instead of the full boolean signature.

Semilattice-ordered semigroups are representable as algebras of binary relations [Bredikhin and Schein] even if we include the residuals of the semigroup operation [Andreka and Mikulas].

As a contrast, we show that algebras of binary relations whose signature includes intersection and composition (the representation of meet and the semigroup operation, respectively) and the conjugates of composition are not finitely axiomatizable.

Date received: December 14, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caig-07.