Ross Willard, University of Waterloo
"Residually finite equational theories"
An equational theory T is said to be residually finite if every model of the theory can be embedded in a product of finite models of the theory. Equivalently, T is residually finite if and only if its irreducible models (those that cannot be embedded in products of “simpler” models) are all finite. In practice, it seems that whenever a theory is both “interesting” and residually finite, then there is a finite upper bound to the sizes of its irreducible models. In other words, we see a sort of compactness principle for “interesting” equational theories: if such a theory has arbitrarily large finite irreducible models, then it must have an infinite irreducible model. Whether or not this observation holds generally has been open for almost 50 years. In this talk I will discuss some recent progress with collaborators Keith Kearnes and Agnes Szendrei.
MC 5479