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- W3169552282 abstract "In this article, we study the lattice of Lawvere-Tierney topologies on Hyland’s effective topos. For this purpose, we introduce a new computability-theoretic reducibility notion, which is a common extension of the notions of Turing reducibility and generalized Weihrauch reducibility. Based on the work by Lee and van Oosten [Ann. Pure Appl. Logic 164 (2013), pp. 866-883], we utilize this reducibility notion for providing a concrete description of the lattice of the Lawvere-Tierney topologies on the effective topos. As an application, we solve several open problems proposed by Lee and van Oosten. For instance, we show that there exists no minimal Lawvere-Tierney topology which is strictly above the identity topology on the effective topos." @default.
- W3169552282 created "2021-06-22" @default.
- W3169552282 creator A5057445953 @default.
- W3169552282 date "2023-01-23" @default.
- W3169552282 modified "2023-09-25" @default.
- W3169552282 title "Lawvere-Tierney topologies for computability theorists" @default.
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- W3169552282 doi "https://doi.org/10.1090/btran/134" @default.
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