Finite Decidability of Locally Finite Varieties
by
Dejan Delic
MPCS, Ryerson University

One of the outstanding problems in the contemporary general algebra has been the quest for the description of locally finite equational theories (i.e. locally finite classes of algebras defined via equalities of terms in a given language) whose first-order theory is decidable.

A class of algebras is considered to be `badly structured' if a structurally rich class of structures, e.g. the class of all (finite) graphs, can be interpreted in it using a scheme of first-order formula with parameters. In universal algebra, this notion is intimately related to the one of decidability, and, in particular, the decidability of the subclass of all finite members. The techniques of tame congruence theory have proved to be the principal tool in this line of investigation. In this talk, we shall outline the structural features of algebras in finitely decidable locally finite varieties.

Date received: April 23, 2004