Representations of countable Krasneralgebras
by
Ferdinand Börner
Universität Potsdam

A relational Krasneralgebra is a set of finitary relations on a basic set A, closed under all first-order definable operations on relations. An abstract Krasneralgebra (KA) is a many-sorted algebraic structure defined by some identities, such that the variety of all KAs is just the variety, generated by all relational KAs.

We investigate representations of countable simple KAs as relational KAs over countable basic sets A. We obtain algebraic statements corresponding to completeness theorems in predicate logic. Among others, we show that omega-categorical KAs correspond to Galois-closed sets of relations (w.r.t. the Galois connection sInv-Aut).

Date received: January 18, 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 # cafo-62.