Paraconsistent Set Theory

Abstract

Intuitively, a set is any collection of elements that satisfy a given property. By allowing arbitrary properties one finds a very flexible way of specifying sets-the method of abstraction. In this method a set is specified by giving the condition that an object must satisfy in order to belong to the set. In this way, the basic axiom known as the "Schema of Comprehension" or "Principle of Comprehension" proposed by Frege in 1893 in the course of his investigations (see [1]) was the following:If φ is a property (denoted by a first-order formula φ(x)) then there exists a set y formed by all elements satisfying property φ, that is, y = {x : φ(x)}.