A preservation theorem for ec-structures with applications

Abstract

AbstractWe characterize the model companions of universal Horn classes generated by a two-element algebra (or ordered two-element algebra). We begin by proving that given two mutually model consistent classes M and N of (respectively ) structures, with , , provided that an -definability condition for the function and relation symbols of holds. We use this, together with Post's characterization of ISP(A), where A is a two-element algebra, to show that the model companions of these classes essentially lie in the classes of posets and semilattices, or characteristic two groups and relatively complemented distributive lattices.