New Formulation of the Axiom of Choice by making use of the Comprehension Operator
Katuzi Ono · Nagoya Mathematical Journal · 1963
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 operator is remarkable in that it can be defined in any formal system having themembershiprelation ∈, which is hereafter called theuniversal systemand is denoted by U. In this work, we would like to point out that theaxiom 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.