Prefilters over an arbitrary Boolean Algebra

Abstract

We define the notion of a prefilter and then proceed to characterize the lattice of prefilters over an arbitrary Boolean Algebra. The lattice theoretic terminology can be found in Gratzer [5] and [6]. In the second section we further investigate the pseudo-prefilter consequence that was defined by Bloom [ ]. We consider arbitrary prefilter matrices and prove a completeness theorem (Theorem 4 of Section II). Our logical terminology is that of Brown and Suszko [4].