Primitive Positive Formulas Excluding Enough Algebraic Operations
by
Jennifer Hyndman
University of Northern British Columbia

I.P. Bestsennyi has shown that a 3-element unary algebra does not have a finite basis for its quasi-equations if and only if it has one of three bad algebras as a term reduct. J. Hyndman and J. Pitkethly have provided equivalent conditions for a 3-element unary algebra to have enough algebraic operations. One of these conditions is the absence of Bestsennyi's bad algebras as an isoreduct. In this talk I extend these results by showing that a unary algebra with a primitive positive formula defining a pp-acyclic relation does not have enough algebraic operations and does not have a finite basis for its quasi-equations.

Date received: February 28, 2003