A Minimal Predicative Set Theory

The central idea of this paper is to perform Nelson's program starting from an extremely weak set theory instead of Robinson's Q. Our theory, which is called N after Nelson, has two non-logical axioms; one asserts the existence of an empty set, the other one asserts that, given two sets x and y, we can form the union of x and the singleton of y. A strictly finitistic proof of the Herbrand consistency of N is given. Moreover, it is shown that Q, and therefore Nelson's Q*, is interpretable in N. Thus Q* is proved by strictly finitistic means to be consistent relative to N.