Clement Wan, Department of Pure Mathematics, University of Waterloo
"Are pseudovarieties the finite models of a set of equations?"
Birkhoff's Theorem tells us that a class of algebras in some signature is equational if and only if it is a variety: that is, closed under homomorphic images, subalgebras, and product algebras. In this talk we will explore the finite case: we will prove a similar correspondence for classes of finite algebras, called pseudovarieties, give an example of this finite case correspondence, and conclude with a connection to an open problem: must a finite algebra that generates a finitely based pseudovariety also generate a finitely based variety? This talk will be accessible with knowledge of basic group theory.
MC 5403