Abstract

We extend to NFU the familiar permutation method used in NF to obtain independence results for unstratified sentences. We apply this technique in order to characterize the theories resulting from the addition to NFU of the supposition that the number of atoms is less or equal to the number of sets or the supposition that the number of atoms is greater or equal to the number of sets. Although we show further that no stratified sentence on sets can be shown independent using this method alone, we prove nevertheless independence results for stratified sentences referring to the set of atoms