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CANTORIAN MODELS OF PREDICATIVE $\mathrm {NF}$

Part of: Set theory

Published online by Cambridge University Press:  13 October 2022

PANAGIOTIS ROUVELAS Open the ORCID record for PANAGIOTIS ROUVELAS [Opens in a new window]
PANAGIOTIS ROUVELAS*
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF PATRAS 26504 RIO PATRAS, GREECE
*
E-mail: [email protected]
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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.

Keywords

set theorySimple Type TheoryTSTTangled Type TheoryNew FoundationsNFpredicative NF

MSC classification

Primary: 03E35: Consistency and independence results 03E70: Nonclassical and second-order set theories
Type
Article
Information
The Journal of Symbolic Logic , Volume 89 , Issue 2 , June 2024 , pp. 637 - 645
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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References

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