Ross Willard, Department of Pure Mathematics, University of Waterloo
“Almost homogeneity and the decidable discriminator variety problem”
An equational class is any class of models in an algebraic signature (i.e., constants and function symbols only) which is axiomatized by universally quantified equations. Such a class is locally finite if every finitely generated substructure of a member is finite. An old problem (going back to Tarski) is the project of describing the locally finite equational classes with finite signature whose first-order theory is decidable. This general problem was reduced to the two following special cases by Burris, McKenzie and Valeriote in the 1980s: (1) modules over finite rings; (2) locally finite discriminator varieties. In this talk I will define discriminator varieties and describe a conjectured characterization of which locally finite discriminator varieties have decidable first-order theory.
MC 5413