The Ordinals

Abstract

were it not for the excessive demands on class existence for the values of y . A trick of inversion (see [l]) obviated the need of infinite values of y in the definition of natural numbers: give the role of y to its complement y (without assuming existence of y) and then reduce. I.e., put bars over the occurrences of y after the quantifier and reduce. The same trick on (1) gives (2) NO(x) for (y)(x G y • S"y Q y O ( 3*)(Us G y y r\ z = A)).