Cantorian Models of Predicative

Journal of Symbolic Logic 89 (2):637-645 (2024)
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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.

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