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CANTORIAN MODELS OF PREDICATIVE
$\mathrm {NF}$
- Part of
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- Journal:
- The Journal of Symbolic Logic / Volume 89 / Issue 2 / June 2024
- Published online by Cambridge University Press:
- 13 October 2022, pp. 637-645
- Print publication:
- June 2024
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- Article
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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.
