Marcel Jackson – Classes defined by quantified equations

La Trobe University

Classes of algebras defined by universally quantified conjunctions of equations are more familiarly known as varieties and provide perhaps the most widely studied framework of understanding in universal algebra. We investigate classes defined instead by arbitrarily quantified conjunctions of equations. We revisit a preservation theorem for this fragment of first order logic, and find amongst other results that it can be used to capture a great many of the well-known non-variety classes of semigroups.
This is primarily joint work with Peter Higgins.