and NFU makes this intuition not directly applicable. However, the intuition of forming sets at a stage from sets developed at earlier stages can be augmented to allow forming sets at a stage consisting of all possible sets but given sets formed at earlier stages, giving an analogous iterative conception of set. There is a fairly simple method for producing models of NFU in bulk. Using well-known techniques of model theory, one can construct a nonstandard model of Zermelo set theory (nothing nearly as strong as full ZFC is needed for the basic technique) on which there is an external automorphism j (not a set of the model) which moves a rank of the cumulative hierarchy of sets. We may suppose without loss of generality that . We talk about the automorphism moving the rank rather than the ordinal because we do not want to assume that every ordinal in the model is the index of a rank. The domain of the model of NFU will be the nonstandard rank . The membership relation of the model of NFU will be It may now be proved that this actually is a model of NFU. Let be a stratified formula in the language of NFU. Choose an assignment of types to all variables in the formula which witnesses the fact that it is stratified. Choose a natural number N greater than all types assigned to variables by this stratification. Expand the formula into a formula in the language of the nonstandard model of Zermelo set theory with automorphism j using the definition of membership in the model of NFU. Application of any power of j to both sides of an equation or membership statement preserves its truth value because j is an automorphism. Make such an application to each atomic formula in in such a way that each variable x assigned type i occurs with exactly applications of j. This is possible thanks to the form of the atomic membership statements derived from NFU membership statements, and to the formula being stratified. Each quantified sentence can be converted to the form (and similarly for existential quantifiers). Carry out this transformation everywhere and obtain a formula in which j is never applied to a bound variable. Choose any free variable y in assigned type i. Apply uniformly to the entire formula to obtain a formula in which y appears without any application