Strongly Extensional Homomorphism of Implicative Semigroups With Apartness

Abstract

The setting of this research is the Bishop's constructive mathematics. Following the ideas of Chan and Shum, exposed in their famous paper "Homomorphisms of implicative semigroups" ([10]), we discuss the homomorphisms between the implicative semigroups S and T with apartness as a continuation of our recently published article [24]. The specificity of this research is the application of Intuitionistic logic instead of Classical. In addition, we concentrate on the structure of the implicative semigroups with appartness and then on their interaction which do not appear in the classical case ([10]). In this paper, the concept of ordered anti-filter has been associated with strongly extensional homomorphisms between such semigroup.