EQUALITY AND COEQUALITY RELATIONS ON THE CARTESIAN PRODUCT O F SETS by DANEL A . ROMANO in Bihac (Yugoslavia)
0. Introduction
The foundations on constructive mathematics, in BISHOP'S sense [l], rest on and comprise the three primitive notions of numbers, classes and computations. We believe that the natural numbers and their basic properties can be understand by any intelligent human being. A class of objects is defined when we are able to describe the construction of its members from a previously constructed object. The notion of an operation of construction is fundamental. We understand that an operation is a finite, concrete object which can be given by a list of instructions. These instructions must be explicit in nature, and must cali only for the performance of "mechanical" computat ions. This paper contains a constructive development of some constructions of an equality and a coequality relation on the Cartesian product of sets, and examples of subgroups and co-subgroups of Cartesian product of Abelian groups. For all notions of sets in constructive mathematics the reader is refered to [I], [2], [5] and [6]. The papers [43 and [lo] contain the elementary definitions, notations and basic facts about finite and infinite sets, and the papers [6] and [7] of Abelian groups in BISHOP'S constructive mathematics which will be used here.