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- W2341084540 abstract "In this paper $mathrm{NFU}^{-mathrm{AC}}$ is used to denote Ronald Jensen's modification of Quine's `New Foundations' Set Theory ($mathrm{NF}$) fortified with a type-level pairing function but without the Axiom of Choice. The axiom $mathrm{AxCount}_geq$ is the variant of the Axiom of Counting which asserts that no finite set is smaller than its own set of singletons. This paper shows that $mathrm{NFU}^{-mathrm{AC}}+mathrm{AxCount}_geq$ proves the consistency of the Simple Theory of Types with Infinity ($mathrm{TSTI}$). This result implies that $mathrm{NF}+mathrm{AxCount}_geq$ proves that consistency of $mathrm{TSTI}$, and that $mathrm{NFU}^{-mathrm{AC}}+mathrm{AxCount}_geq$ proves the consistency of $mathrm{NFU}^{-mathrm{AC}}$." @default.
- W2341084540 created "2016-06-24" @default.
- W2341084540 creator A5046351134 @default.
- W2341084540 date "2016-01-16" @default.
- W2341084540 modified "2023-09-27" @default.
- W2341084540 title "On the strength of a weak variant of the Axiom of Counting" @default.
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