Graduate School of Mathematics | Nagoya University

Index

[Preprints]  [Publications]  [Unpublished Notes]  [Publications in Japanese]  [Magazine Articles]

Preprints

  1. The gamified Katetov order is not linear (in fact, very much not so) (with M. Ng)
    preprint. [arXiv]
  2. On the strength of the double negation elimination for classical Σk-formulas (with M. Fujiwara and S. Nakata)
    in preparation.
  3. Modified realizability subtoposes via total Weihrauch reducibility (with A. Kajikawa, M. Kaku, S. Nakata)
    in preparation.
  4. The game-theoretic Katetov order and idealised effective subtoposes (with M. Ng)
    preprint. [arXiv]
  5. The infinite loop operation and the axiom of dependent choice
    in preparation.
  6. Towards higher order Weihrauch reducibility (with M. Obayashi)
    in preparation.
  7. The fourth level of the realizability-theoretic arithmetical hierarchy (with G. Glowacki and K. Takayanagi)
    in preparation.
    Category: degree theory, realizability
  8. The arithmetical hierarchy: A realizability-theoretic perspective
    preprint, 43 pages. [arXiv]
    Category: degree theory, realizability
  9. Church's thesis in subtoposes of the effective topos (with K. M. Ng)
    in preparation.
    Category: constructive reverse mathematics, degree theory, realizability, topos
  10. Degree structures of function spaces over unusual ground types I, II (with K. M. Ng)
    in preparation, 56 pages.
    Category: degree theory, computable topology
  11. De Groot-like duality for represented spaces (with A. Pauly)
    in preparation, 35 pages.
    Category: computable topology, synthetic topology
  12. Rethinking the notion of oracle: A prequel to Lawvere-Tierney topologies for computability theorists
    submitted, 57 pages. [arXiv]
    Category: topos theory, Weihrauch lattice
  13. On some topics around the Wadge rank ω2
    submitted, 31 pages. [arXiv]
    Category: descriptive set theory
  14. Degrees of incomputability, realizability and constructive reverse mathematics
    in preparation, 34 pages. [arXiv]
    Category: constructive reverse mathematics, Weihrauch lattice

Publications

  1. What can Topology tell us about Logical Complexity? (with M. Ng)
    to appear in the Proceedings of the 15th Panhellenic Logic Symposium. [arXiv]
  2. The subTuring degrees (with K. M. Ng)
    to appear in Canadian Journal of Mathematics, 29 pages. [arXiv] [doi]
    Category: degree theory, realizability
  3. Many-one reducibility with realizability
    to appear in Journal of Symbolic Logic, 39 pages. [arXiv] [doi]
    Category: degree theory, realizability
  4. Enumeration degrees and non-metrizable topology (with K. M. Ng, and A. Pauly)
    to appear in Memoirs of the American Mathematical Society. [arXiv]
    Category: topological aspects of computability theory, degree theory
  5. Degree spectra of homeomorphism types of Polish spaces (with M. Hoyrup, and V. Selivanov)
    to appear in Journal of Symbolic Logic. [arXiv] [doi]
    Category: computable topology
  6. Ideal presentations and numberings of some classes of effective quasi-Polish spaces (with M. de Brecht and V. Selivanov)
    Computability, 13 (2024), no. 3-4, pp. 325-348. [arXiv] [doi]
    Category: computable topology
  7. 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]
    Category: temporal logic
  8. On the main scientific achievements of Victor Selivanov (with N. Bazhenov, S. Selivanova and D. Spreen)
    Computability, 12 (2023), no. 4, 301-314. [doi]
  9. De Groot duality for represented spaces (with A. Pauly)
    In Proceedings of CiE 2023, Lecture Notes in Computer Science, 13967 (2023), 89-101. [doi]
    Category: computable topology
  10. Lawvere-Tierney topologies for computability theorists
    Transactions of the American Mathematical Society, Series B, 10 (2023), 48-85. [arXiv] [doi]
    Category: topos theory, Weihrauch lattice
  11. 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]
    Category: descriptive set theory
  12. Point degree spectra of represented spaces (with A. Pauly)
    Forum of Mathematics, Sigma, 10 (2022), e31, 1-27. [arXiv] [doi]
    Category: descriptive set theory, topological dimension theory, application of computability theory
  13. 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]
    Category: descriptive set theory, BQO theory
  14. Topological reducibilities for discontinuous functions and their structures
    Israel Journal of Mathematics, 252 (2022), pp. 461-500. [arXiv] [doi]
    Category: descriptive set theory, computability theory
  15. 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]
    Category: computable topology
  16. 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]
    Category: Weihrauch lattice
  17. 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]
    Category: descriptive set theory, application of computability theory
  18. 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]
    Category: Weihrauch lattice
  19. 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]
    Category: descriptive set theory
  20. The Brouwer invariance theorems in reverse mathematics
    Forum of Mathematics, Sigma, 8 (2020), Paper No. e51, 12 pages. [arXiv] [doi]
    Category: reverse mathematics
  21. 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]
    Category: computable topology
  22. On a metric generalization of the tt-degrees and effective dimension theory
    Journal of Symbolic Logic, 84 (2) (2019), pp. 726-749. [arXiv] [doi]
    Category: topological aspects of computability theory, Kolmogorov complexity
  23. 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]
    Category: descriptive set theory, BQO theory, application of computability theory
  24. 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]
    Category: Weihrauch lattice
  25. 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]
    Category: constructive reverse mathematics
  26. 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]
    Category: computability theory, degree theory, BQO theory
  27. 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]
    Category: computable analysis
  28. 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]
    Category: higher computability theory, higher randomness
  29. Borel-piecewise continuous reducibility for uniformization problems
    Logical Methods in Computer Science, 12 (4) (2016), pp. 1-35. [arXiv] [doi]
    Category: discontinuous functions, computable analysis
  30. 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]
    Category: Weihrauch lattice
  31. Decomposing Borel functions using the Shore-Slaman join theorem
    Fundamenta Mathematicae, 230 (2015), pp. 1-13. [doi]
    Category: descriptive set theory, application of computability theory
  32. Unified characterizations of lowness properties via Kolmogorov complexity (with K. Miyabe)
    Archive for Mathematical Logic, 54 (3-4) (2015), pp. 329-358. [doi]
    Category: algorithmic randomness
  33. Comparing the Medvedev and Turing degrees of Π01 classes
    Mathematical Structures in Computer Science, 25 (8) (2015), pp. 1649-1668. [doi]
    Category: degree theory
  34. 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]
    Category: degree theory, Weihrauch lattice
  35. 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]
    Category: computability theory, discontinuous functions
  36. Uniform Kurtz randomness (with K. Miyabe)
    Journal of Logic and Computation, 24 (4) (2014), pp. 863-882. [doi]
    Category: algorithmic randomness
  37. 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]
    Category: computable measure theory
  38. On the strength of marriage theorems and uniformity (with M. Fujiwara and K. Higuchi)
    Mathematical Logic Quarterly, 60 (3) (2014) pp. 136-153. [doi]
    Category: reverse mathematics
  39. Effective strong nullness and effectively closed sets (with K. Higuchi)
    In Procedings of CiE 2012, Lecture Notes in Computer Science, 7318 (2012), pp. 304-313. [doi]
    Category: degree theory, computable measure theory
  40. A hierarchy of immunity and density for sets of reals
    In Procedings of CiE 2012, Lecture Notes in Computer Science, 7318 (2012), pp. 385-395. [doi]
    Category: degree theory
  41. Incomputability of simply connected planar continua
    Computability, 1 (2) (2012), pp. 131-152. [doi]
    Category: computable topology
  42. The ∀∃-theory of the effectively closed Medvedev degrees is decidable (with J. A. Cole)
    Archive for Mathematical Logic, 49 (2010), pp. 1-16. [doi]
    Category: degree theory
  43. Immunity and non-cupping for closed sets (with D. Cenzer, R. Weber and G. Wu)
    Tbilisi Mathematical Journal, 2 (2009), pp. 77-94.
    Category: degree theory

Unpublished Notes

  1. Convex choice, finite choice, and sorting (with A. Pauly)
    submitted in May 2019, 23 pages. [arXiv]
    Category: Weihrauch lattice
  2. Effective forcing with Cantor manifolds
    A draft in Feb. 2017.
  3. A priority argument in descriptive set theory: A very detailed exposition of Semmes' proof
    First draft in 2014, Second draft in 2016, Current version in Feb. 2018.
    Category: descriptive set theory, application of computability theory
  4. Null additivity in the theory of algorithmic randomness (with K. Miyabe)
    written in 2014, submitted to MLQ, rejected in Feb. 2016.
    Category: generalized computability theory, algorithmic randomness
  5. A hybridization of two Baire hierarchies of Borel functions
    unpublished, 2012.
    Category: descriptive set theory, application of computability theory
  6. Notes on ∀∃!-conservation (with Wei Wang)
    unpublished, 2011.
    Category: reverse mathematics

Publications in Japanese

  1. An application of computability theory to decomposability problem on Borel functions: an extended abstract (in Japanese)
    New Trends in Theoretical Computer Science, RIMS Kokyuroku (proceedings), Kyoto University 1849 (2013), pp. 32-36.
    Category: descriptive set theory, application of computability theory
  2. Set theory of the real line and algorithmic randomness: a survey (in Japanese)
    Proof Theory and Complexity, RIMS Kokyuroku (proceedings), Kyoto University 1832 (2013), pp. 97-113.
    Category: cardinal invariants, algorithmic randomness
  3. Computability theory of continua (in Japanese)
    Formal Systems and Computability Theory, RIMS Kokyuroku (proceedings), Kyoto University 1729 (2011), pp. 48-66.
    Category: computable topology
  4. Notes on reverse recursion theory and reverse mathematics (in Japanese)
    Proof Theoretical Study of the Structure of Logic and Computation, RIMS Kokyuroku (proceedings), Kyoto University 1635 (2009), pp. 51-59.
    Category: reverse mathematics, reverse recursion theory

Magazine Articles (for the General Public, written in Japanese)

  1. Size Issues for Categories
    Sugaku Seminar (Math Seminar Magazine) Nov. 2025 Issue, Nippon Hyoron Sha.
  2. Important Sets of Lebesgue Measure Zero
    Sugaku Seminar (Math Seminar Magazine) Nov. 2024 Issue, Nippon Hyoron Sha.
  3. Rigor, Abstraction, and Development of "Computability" in Mathematics
    Gendai Siso (Contemporary Philosophy) Jul. 2023 Issue, Seido Sha, pp. 51-63.
  4. Descriptive Set Theory / Beyond Borel Sets
    Suuri Kagaku (Mathematical Sciences Magazine) Jun. 2022 Issue, Science-Sha.
  5. Foundations of Mathematics and Computability
    Suuri Kagaku (Mathematical Sciences Magazine) Aug. 2021 Issue, Science-Sha, pp. 58-64.
  6. The Heart of Reverse Mathematics / Don't be Monochrome, Be Colorful
    Sugaku Seminar (Math Seminar Magazine) Feb. 2021 Issue, Nippon Hyoron Sha, pp. 15-19.
  7. Hilbert's Tenth Problem and its Companions
    Sugaku Seminar (Math Seminar Magazine) Nov. 2020 Issue, Nippon Hyoron Sha, pp. 24-26.
  8. Calling the Name of Infinity: A Short History of Mathematics Surrounding Fast Growing Functions
    Gendai Siso (Contemporary Philosophy) Dec. 2019 Issue, Seido Sha, pp. 19-28.
  9. The Ackermann Function and Hilbert
    Sugaku Seminar (Math Seminar Magazine) Jul. 2019 Issue, Nippon Hyoron Sha, pp. 22-27.