Computability Learning Seminar

Michael Gregory, University of Waterloo

Basic Universal Algebra Aimed at Isomorphism Problems for c.e. Presentations

We begin with the notions of a universal algebra, homomorphism, congruence, and quotient algebra, and discuss the relationship between congruences and homomorphic images. We then introduce term algebras and varieties, culminating in a statement of Birkhoff's HSP Theorem. To prepare for later computability applications, we briefly review lattices and the congruence lattice of an algebra. Finally, we describe how finitely generated and computably enumerable algebras may be specified by presentations.

MC 5403