Standard topological quasi-varieties - examples and problems
by
Miroslav Haviar
M. Bel University
Coauthors: David M. Clark (SUNY, New Paltz), Brian A. Davey (La Trobe University, Melbourne), Jane G. Pitkethly (La Trobe University, Melbourne), Rashed M. Talukder (La Trobe University, Melbourne)

The introduction of standard topological quasi-varieties has been motivated by the theory of natural dualities, which provides a tight connection between a given quasi-variety of algebras and its dual topological quasi-variety. We initiate a program of study to determine which choices of the topological quasi-variety are standard and which are not. We say that a topological quasi-variety is standard if, in an appropriate sense, there is a nice axiomatic description of its members which allows us to recognize them by looking only at their finite substructures. The study lies at the confluence of algebra, topology and mathematical logic, and has been initiated by the Duality Research Group at La Trobe University (Melbourne) in 2000.

Date received: April 12, 2002

Copyright © 2002 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 # caiv-12.