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Transactions of the American Mathematical Society Series B

Published by the American Mathematical Society since 2014, this gold open access electronic-only journal is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 2330-0000

The 2020 MCQ for Transactions of the American Mathematical Society Series B is 1.73.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Lawvere-Tierney topologies for computability theorists
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by Takayuki Kihara
Trans. Amer. Math. Soc. Ser. B 10 (2023), 48-85
DOI: https://doi.org/10.1090/btran/134
Published electronically: January 23, 2023

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.
References
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Bibliographic Information
  • Takayuki Kihara
  • Affiliation: Graduate School of Informatics, Nagoya University, Nagoya, 464-8601 Japan
  • MR Author ID: 892476
  • ORCID: 0000-0002-1611-952X
  • Email: kihara@i.nagoya-u.ac.jp
  • Received by editor(s): July 6, 2021
  • Received by editor(s) in revised form: August 19, 2022, and August 24, 2022
  • Published electronically: January 23, 2023
  • Additional Notes: The author was partially supported by JSPS KAKENHI Grant Numbers 19K03602, 21H03392 and 22K03401, and the JSPS-RFBR Bilateral Joint Research Project JPJSBP120204809.
  • © Copyright 2023 by the author under Creative Commons Attribution 3.0 License (CC BY 3.0)
  • Journal: Trans. Amer. Math. Soc. Ser. B 10 (2023), 48-85
  • MSC (2020): Primary 03D30; Secondary 03D80, 18B25
  • DOI: https://doi.org/10.1090/btran/134
  • MathSciNet review: 4538503