On NFU

Abstract

We first describe a general method for building models of NFU, i.e. NF with atoms, without the help of Ramsey’s theorem. Then, we show that NFU has essentially the same strength as NF without the axiom of extensionality. Further, we consider axioms stating that there is a set extensionally equivalent to every nonextensional object. By using a variant of the technique of permutations, we prove the consistency of such axioms of weak extensionality with the stratifiable axioms of comprehension. Finally, we show that there is an axiom of weak extensionality that implies full extensionality. © 1992 by the University of Notre Dame. All Rights Reserved.