Quotient of a Consistent Subset by an Element - Constructive Point of View
Daniel A. Romano, Mladen Stojanovic · 2008
Consistent subset of a semigroup is important subset of semigroups in Bishop’s constructive mathematics. In this article we introduce no-tion of quotient [A: x] of consistent subset A by an element x of commu-tative semigroup and research its properties. Besides, we give (without the axiom of choose) a construction of the maximal strongly extensional consistent subset C(x) of semigroup for any element x of semigroup such that x C(x). At the end of this investigation, we give some applica-tions.