New Formulation of the Axiom of Choice by making use of the Comprehension Operator

Abstract

We have introduced in our former work [1] and [2] the comprehension operator “{·)”, which maps every binary relation to a binary relation. The definition of this operatoris remarkable in that it can be defined in any formal system having the membership relation ∈, which is hereafter called the universal system and is denoted by U. In this work, we would like to point out that the axiom of choice, in the strong sense as well as in the weak sense, can be formulated in an extremely simple style by making use of the comprehension operator.