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- W4299892316 abstract "The notion of slow provability for Peano Arithmetic ($mathsf{PA}$) was introduced by S.D. Friedman, M. Rathjen, and A. Weiermann. They studied the slow consistency statement $mathrm{Con}_{mathsf{s}}$ that asserts that a contradiction is not slow provable in $mathsf{PA}$. They showed that the logical strength of $mathsf{PA}+mathrm{Con}_{mathsf{s}}$ lies strictly between that of $mathsf{PA}$ and $mathsf{PA}$ together with its ordinary consistency: $mathsf{PA}subsetneq mathsf{PA}+mathrm{Con}_{mathsf{s}}subsetneq mathsf{PA}+mathrm{Con}$. This paper is a further investigation into slow provability and its interplay with ordinary provability in $mathsf{PA}$. We study three variants of slow provability. The associated consistency statement of each of these yields a theory that lies strictly between $mathsf{PA}$ and $mathsf{PA}+mathrm{Con}$ in terms of logical strength. We investigate Turing-Feferman progressions based on these variants of slow provability. We show that for our three notions, the Turing-Feferman progression reaches $mathsf{PA}+mathrm{Con}$ in a different numbers of steps, namely $varepsilon_0$, $omega$, and $2$. For each of the three slow provability predicates, we also determine its joint provability logic with ordinary $mathsf{PA}$-provability." @default.
- W4299892316 created "2022-10-03" @default.
- W4299892316 creator A5023087680 @default.
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- W4299892316 date "2016-02-04" @default.
- W4299892316 modified "2023-10-18" @default.
- W4299892316 title "Slow and Ordinary Provability for Peano Arithmetic" @default.
- W4299892316 doi "https://doi.org/10.48550/arxiv.1602.01822" @default.
- W4299892316 hasPublicationYear "2016" @default.
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