Perception of BCC-algebras under the Bishop’s principled-philosophical orientation: BCC-algebra with apartness.

Abstract

In this paper it is  given a short introduction in a reconsideration about BCC-algebras under the light of Bishop's principled-philosophical orientation. At the first, it is introduced  the concept of BCC-algebras into this orientation. Additionally, the consequences of the selected axioms in the determination of BCC-algebras with apartness are analyzed.
Also, some substructures in the BCC-algebras with apartness that have no counterparts in the classical case and which appear as products of the chosen logical environment such as co-ideals are analyzed.
At the end, a result that can be viewed as the isomorphism theorem in such BCC-algebras are exposed.