Abstract

Tangled Type Theory was introduced by Randall Holmes in [3] as a new way of approaching the consistency problem for$\mathrm {NF}$. Although the task of finding models for this theory is far from trivial (considering it is equiconsistent with$\mathrm {NF}$), ways of constructing models for certain fragments of it have been discovered. In this article, we present a simpler way of constructing models of predicative Tangled Type Theory and consequently of predicative$\mathrm {NF}$. In these new models of predicative$\mathrm {NF}$, the universe is well-orderable and equinumerous to the set of singletons.