国立大学法人 名古屋大学 | 大学院情報学研究科 | 数理情報学専攻 | 数理情報基礎論講座

Preprints

  1. The fourth level of the realizability-theoretic arithmetical hierarchy (with G. Glowacki and K. Takayanagi)
    in preparation.
  2. The arithmetical hierarchy: A realizability-theoretic perspective
    in preparation, 43 pages. [arXiv]
  3. Church's thesis in subtoposes of the effective topos (with K. M. Ng)
    in preparation.
  4. The subTuring degrees (with K. M. Ng)
    in preparation, 22 pages. [arXiv]
  5. Degree structures of function spaces over unusual ground types (with K. M. Ng)
    in preparation, 56 pages.
  6. De Groot-like duality for represented spaces (with A. Pauly)
    in preparation, 35 pages.
  7. Rethinking the notion of oracle: A prequel to Lawvere-Tierney topologies for computability theorists
    submitted, 57 pages. [arXiv]
  8. On some topics around the Wadge rank ω2
    submitted, 31 pages. [arXiv]
  9. Degrees of incomputability, realizability and constructive reverse mathematics
    preprint, 34 pages. [arXiv]
  10. Convex choice, finite choice, and sorting (with A. Pauly)
    submitted, 23 pages. [arXiv]

Publications

  1. Many-one reducibility with realizability
    to appear in Journal of Symbolic Logic, 36 pages. [arXiv]
  2. Enumeration degrees and non-metrizable topology (with K. M. Ng, and A. Pauly)
    to appear in Memoirs of the American Mathematical Society. [arXiv]
  3. On the metric temporal logic for continuous stochastic processes (with M. Ikeda and Y. Yamagata)
    Logical Methods in Computer Science, 20 (2024), Issue 2, pp. 14:1-14:35. [arXiv] [doi]
  4. Ideal presentations and numberings of some classes of effective quasi-Polish spaces (with M. de Brecht, and V. Selivanov)
    to appear in Computability. [arXiv] [doi]
  5. Degree spectra of homeomorphism types of compact Polish spaces (with M. Hoyrup, and V. Selivanov)
    to appear in Journal of Symbolic Logic. [arXiv] [doi]
  6. On the main scientific achievements of Victor Selivanov (with N. Bazhenov, S. Selivanova and D. Spreen)
    Computability, 12 (2023), no. 4, 301-314. [doi]
  7. De Groot duality for represented spaces (with A. Pauly)
    In Proceedings of CiE 2023, Lecture Notes in Computer Science, 13967 (2023), 89-101. [doi]
  8. Lawvere-Tierney topologies for computability theorists
    Transactions of the American Mathematical Society, Series B, 10 (2023), 48-85. [arXiv] [doi]
  9. A syntactic approach to Borel functions: Some extensions of Louveau's theorem (with K. Sasaki)
    Archive for Mathematical Logic, 62 (2023), 1041-1082. [arXiv] [doi]
  10. Point degree spectra of represented spaces (with A. Pauly)
    Forum of Mathematics, Sigma, 10 (2022), e31, 1-27. [arXiv] [doi]
  11. Wadge-like degrees of Borel bqo-valued functions (with V. Selivanov)
    Proceedings of the American Mathematical Society, 150 (2022), no. 9, 3989-4003. [arXiv] [doi]
  12. Topological reducibilities for discontinuous functions and their structures
    Israel Journal of Mathematics, 252 (2022), pp. 461-500. [arXiv] [doi]
  13. Enumerating classes of effective quasi-Polish spaces (with M. de Brecht and V. Selivanov)
    In Proceedings of CiE 2022, Lecture Notes in Computer Science, 13359 (2022), pp. 88-102. [doi]
  14. A comparison of various analytic choice principles (with P.-E. Anglès d'Auriac)
    Journal of Symbolic Logic, 86 (2021), no. 4, 1452-1485. [arXiv] [doi]
  15. Turing degrees in Polish spaces and decomposability of Borel functions (with V. Gregoriades and K. M. Ng)
    Journal of Mathematical Logic 21 (2021), no. 1, 2050021, 41 pages. [arXiv] [doi]
  16. Searching for an analogue of ATR0 in the Weihrauch lattice (with A. Marcone, and A. Pauly)
    Journal of Symbolic Logic 85 (2020), no. 3, 1006–1043. [arXiv] [doi]
  17. Decomposing functions of Baire class 2 on Polish spaces (with L. Ding, B. Semmes, and J. Zhao)
    Journal of Symbolic Logic 85 (2020), no. 3, 960–971. [arXiv] [doi]
  18. The Brouwer invariance theorems in reverse mathematics
    Forum of Mathematics, Sigma 8 (2020), Paper No. e51, 12 pages. [arXiv] [doi]
  19. Degrees of non-computability of homeomorphism types of Polish spaces (with M. Hoyrup, and V. Selivanov)
    In Proceedings of CiE 2020, Lecture Notes in Computer Science 12098 (2020), pp. 189-192. [doi]
  20. On a metric generalization of the tt-degrees and effective dimension theory
    Journal of Symbolic Logic 84 (2) (2019), pp. 726-749. [arXiv] [doi]
  21. On the structure of the Wadge degrees of BQO-valued Borel functions (with A. Montalbán)
    Transactions of the American Mathematical Society 371 (11) (2019), pp. 7885-7923. [arXiv] [doi]
  22. Finite choice, convex choice and sorting (with A. Pauly)
    In Proceedings of TAMC 2019, Lecture Notes in Computer Science, 11436 (2019), pp. 378-393. [doi]
  23. The binary expansion and the intermediate value theorem in constructive reverse mathematics (with J. Berger, H. Ishihara and T. Nemoto)
    Archive for Mathematical Logic 58 (1-2) (2019), pp. 203-217. [doi]
  24. The uniform Martin's conjecture for many-one degrees (with A. Montalbán)
    Transactions of the American Mathematical Society 370 (12) (2018), pp. 9025-9044. [arXiv] [doi]
  25. Computability of subsets of metric spaces (with Z. Iljazović)
    In: Brattka V., Hertling P. (eds) Handbook of Computability and Complexity in Analysis, Theory and Applications of Computability (In cooperation with the association Computability in Europe). Springer, Cham., pp. 29-69. [doi]
  26. Higher randomness and lim-sup forcing within and beyond hyperarithmetic
    In Sets and Computations, Lecture Notes Series, IMS, NUS 33 (2017), pp. 117-155. [doi]
  27. Borel-piecewise continuous reducibility for uniformization problems
    Logical Methods in Computer Science 12 (4) (2016), pp. 1-35. [arXiv] [doi]
  28. Dividing by zero -- how bad is it, really? (with A. Pauly)
    In Proceedings of MFCS 2016, Leibniz International Proceedings in Informatics 58 (2016), pp. 58:1-58:14. [arXiv] [doi]
  29. Decomposing Borel functions using the Shore-Slaman join theorem
    Fundamenta Mathematicae 230 (2015), pp. 1-13. [doi]
  30. Unified characterizations of lowness properties via Kolmogorov complexity (with K. Miyabe)
    Archive for Mathematical Logic 54 (3-4) (2015), pp. 329-358. [doi]
  31. Comparing the Medvedev and Turing degrees of Π01 classes
    Mathematical Structures in Computer Science 25 (8) (2015), pp. 1649-1668. [doi]
  32. Inside the Muchnik degrees II: The degree structures induced by the arithmetical hierarchy of countably continuous functions (with K. Higuchi)
    Annals of Pure and Applied Logic 165 (6) (2014), pp. 1201-1241. [doi]
  33. Inside the Muchnik degrees I: Discontinuity, learnability, and constructivism (with K. Higuchi)
    Annals of Pure and Applied Logic 165 (5) (2014), pp. 1058-1114. [doi]
  34. Uniform Kurtz randomness (with K. Miyabe)
    Journal of Logic and Computation 24 (4) (2014), pp. 863-882. [doi]
  35. On effectively closed sets of effective strong measure zero (with K. Higuchi)
    Annals of Pure and Applied Logic 165 (9) (2014), pp. 1445-1469. [doi]
  36. On the strength of marriage theorems and uniformity (with M. Fujiwara and K. Higuchi)
    Mathematical Logic Quarterly 60 (3) (2014) pp. 136-153. [doi]
  37. Effective strong nullness and effectively closed sets (with K. Higuchi)
    How the World Computes (CiE 2012), Lecture Notes in Computer Science 7318 (2012), pp. 304-313. [doi]
  38. A hierarchy of immunity and density for sets of reals
    How the World Computes (CiE 2012), Lecture Notes in Computer Science 7318 (2012), pp. 385-395. [doi]
  39. Incomputability of simply connected planar continua
    Computability 1 (2) (2012), pp. 131-152. [doi]
  40. The ∀∃-theory of the effectively closed Medvedev degrees is decidable (with J. A. Cole)
    Archive for Mathematical Logic 49 (2010), pp. 1-16. [doi]
  41. Immunity and non-cupping for closed sets (with D. Cenzer, R. Weber and G. Wu)
    Tbilisi Mathematical Journal 2 (2009), pp. 77-94.

Unpublished Notes

  1. Effective forcing with Cantor manifolds
    A draft in Feb. 2017.
  2. A priority argument in descriptive set theory: A very detailed exposition of Semmes' proof
    First draft in 2014, Current version in Feb. 2018.
  3. Null additivity in the theory of algorithmic randomness (with K. Miyabe)
    unpublished, 2014.
  4. Notes on ∀∃!-conservation (with Wei Wang)
    unpublished, 2011.

Publications in Japanese

  1. ボレル関数の分解問題への計算論の応用(アブストラクト)
    理論計算機科学の新展開, 京都大学数理解析研究所講究録 1849 (2013), pp. 32-36.
  2. 実数の集合論とランダムネス(概説)
    証明論と複雑性, 京都大学数理解析研究所講究録 1832 (2013), pp. 97-113.
  3. 連続体の計算可能性理論
    形式体系と計算理論, 京都大学数理解析研究所講究録 1729 (2011), pp. 48-66.
  4. 逆数学と逆再帰理論について
    証明論と論理・計算の構造, 京都大学数理解析研究所講究録 1635 (2009), pp. 51-59.

Miscellaneous

  1. 重要な意味をもつ測度0の集合はあるか
    数学セミナー 2024年11月号，日本評論社.
  2. ヒルベルトの第10問題とその仲間たち
    数学セミナー編集部 編，数学者の選ぶ「とっておきの数学」，日本評論社.
  3. 数学における《計算可能性》の厳密化、抽象化、そして発展
    現代思想 2023年7月号，青土社, pp. 51-63.
  4. 記述集合論／ボレル集合を超えて
    数理科学 2022年6月号，サイエンス社.
  5. 数学基礎論と計算可能性
    数理科学 2021年8月号，サイエンス社, pp. 58-64.
  6. 逆数学のこころ／白黒ではなく色鮮やかに
    数学セミナー 2021年2月号，日本評論社, pp. 15-19.
  7. ヒルベルトの第10問題とその仲間たち
    数学セミナー 2020年11月号，日本評論社, pp. 24-26.
  8. 無限の名を呼ぶ――巨大関数をとりまく数学小史
    現代思想 2019年12月号，青土社, pp. 19-28.
  9. アッカーマン関数とヒルベルト
    数学セミナー 2019年7月号，日本評論社, pp. 22-27.