Constructive Semigroups with Apartness: Towards a New Algebraic Theory

Abstract

© 2019 Published under licence by IOP Publishing Ltd. The theory of constructive semigroups with apartness is a new approach to semigroup theory, and not a new class of semigroups. Of course, our work is partly inspired by classical semigroup theory, but, on the other hand, it is distinguished from it by two significant aspects: first, we use intuitionistic logic rather than classical, secondly, our work is based on the notion of apartness (between elements, elements and sets). Here, the focus is on E. Bishop's approach to constructive mathematics (BISH), [4].