Department of Mathematical Informatics | Graduate School of Informatics | Nagoya University

Index

[Preprints]  [Publications]  [Unpublished Notes]  [Publications in Japanese]  [Magazine Articles]

Preprints

  1. The fourth level of the realizability-theoretic arithmetical hierarchy (with G. Glowacki and K. Takayanagi)
    in preparation.
    Category: degree theory, realizability
  2. The arithmetical hierarchy: A realizability-theoretic perspective
    in preparation, 43 pages. [arXiv]
    Category: degree theory, realizability
  3. Church's thesis in subtoposes of the effective topos (with K. M. Ng)
    in preparation.
    Category: constructive reverse mathematics, degree theory, realizability, topos
  4. The subTuring degrees (with K. M. Ng)
    in preparation, 22 pages. [arXiv]
    Category: degree theory, realizability
  5. Degree structures of function spaces over unusual ground types (with K. M. Ng)
    in preparation, 56 pages.
    Category: degree theory, computable topology
  6. De Groot-like duality for represented spaces (with A. Pauly)
    in preparation, 35 pages.
    Category: computable topology, synthetic topology
  7. Rethinking the notion of oracle: A prequel to Lawvere-Tierney topologies for computability theorists
    submitted, 57 pages. [arXiv]
    Category: synthetic descriptive set theory, topos theory, Weihrauch lattice
  8. On some topics around the Wadge rank ω2
    submitted, 31 pages. [arXiv]
    Category: descriptive set theory
  9. Degrees of incomputability, realizability and constructive reverse mathematics
    in preparation, 34 pages. [arXiv]
    Category: constructive reverse mathematics, Weihrauch lattice
  10. Convex choice, finite choice, and sorting (with A. Pauly)
    submitted in May 2019, 23 pages. [arXiv]
    Category: Weihrauch lattice

Publications

  1. Many-one reducibility with realizability
    to appear in Journal of Symbolic Logic, 36 pages. [arXiv]
    Category: degree theory, realizability
  2. 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
  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]
    Category: temporal logic
  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]
    Category: computable topology
  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. 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]
    Category: computable topology
  8. 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
  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]
    Category: descriptive set theory
  10. 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
  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]
    Category: descriptive set theory, BQO theory
  12. 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
  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]
    Category: computable topology
  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]
    Category: Weihrauch lattice
  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]
    Category: descriptive set theory, application of computability theory
  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]
    Category: Weihrauch lattice
  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]
    Category: descriptive set theory
  18. The Brouwer invariance theorems in reverse mathematics
    Forum of Mathematics, Sigma, 8 (2020), Paper No. e51, 12 pages. [arXiv] [doi]
    Category: reverse mathematics
  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]
    Category: computable topology
  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]
    Category: topological aspects of computability theory, Kolmogorov complexity
  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]
    Category: descriptive set theory, BQO theory, application of computability theory
  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]
    Category: Weihrauch lattice
  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]
    Category: constructive reverse mathematics
  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]
    Category: computability theory, degree theory, BQO theory
  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]
    Category: computable analysis
  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]
    Category: higher computability theory, higher randomness
  27. 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
  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]
    Category: Weihrauch lattice
  29. 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
  30. 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
  31. Comparing the Medvedev and Turing degrees of Π01 classes
    Mathematical Structures in Computer Science, 25 (8) (2015), pp. 1649-1668. [doi]
    Category: degree theory
  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]
    Category: degree theory, Weihrauch lattice
  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]
    Category: computability theory, discontinuous functions
  34. Uniform Kurtz randomness (with K. Miyabe)
    Journal of Logic and Computation, 24 (4) (2014), pp. 863-882. [doi]
    Category: algorithmic randomness
  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]
    Category: computable measure theory
  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]
    Category: reverse mathematics
  37. 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
  38. 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
  39. Incomputability of simply connected planar continua
    Computability, 1 (2) (2012), pp. 131-152. [doi]
    Category: computable topology
  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]
    Category: degree theory
  41. 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. 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, Second draft in 2016, Current version in Feb. 2018.
    Category: descriptive set theory, application of computability theory
  3. 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
  4. 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. Important Sets of Lebesgue Measure Zero
    Sugaku Seminar (Math Seminar Magazine) Nov. 2024 Issue, Nippon Hyoron Sha.
  2. Rigor, Abstraction, and Development of "Computability" in Mathematics
    Gendai Siso (Contemporary Philosophy) Jul. 2023 Issue, Seido Sha, pp. 51-63.
  3. Descriptive Set Theory / Beyond Borel Sets
    Suuri Kagaku (Mathematical Sciences Magazine) Jun. 2022 Issue, Science-Sha.
  4. Foundations of Mathematics and Computability
    Suuri Kagaku (Mathematical Sciences Magazine) Aug. 2021 Issue, Science-Sha, pp. 58-64.
  5. 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.
  6. Hilbert's Tenth Problem and its Companions
    Sugaku Seminar (Math Seminar Magazine) Nov. 2020 Issue, Nippon Hyoron Sha, pp. 24-26.
  7. 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.
  8. The Ackermann Function and Hilbert
    Sugaku Seminar (Math Seminar Magazine) Jul. 2019 Issue, Nippon Hyoron Sha, pp. 22-27.