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

Index

[Preprints]  [Publications]  [Unpublished Notes]  [Publications in Japanese]  [Magazine Articles]

Preprints

  1. Rethinking the notion of oracle: A link between synthetic descriptive set theory and effective topos theory
    preprint, 51 pages. [arXiv]
    Category: synthetic descriptive set theory, topos theory, Weihrauch lattice
  2. Lawvere-Tierney topologies for computability theorists
    preprint, 35 pages. [arXiv]
    Category: topos theory, Weihrauch lattice
  3. On some topics around the Wadge rank ω2
    preprint, 31 pages. [arXiv]
    Category: descriptive set theory
  4. A syntactic approach to Borel functions: Some extensions of Louveau's theorem (with K. Sasaki)
    submitted, 31 pages. [arXiv]
    Category: descriptive set theory
  5. Degree spectra of homeomorphism types of Polish spaces (with M. Hoyrup, and V. Selivanov)
    submitted in April 2020, 30 pages. [arXiv]
    Category: computable topology
  6. Degrees of incomputability, realizability and constructive reverse mathematics
    in preparation, 34 pages. [arXiv]
    Category: constructive reverse mathematics, Weihrauch lattice
  7. Convex choice, finite choice, and sorting (with A. Pauly)
    submitted in May 2019, 23 pages. [arXiv]
    Category: Weihrauch lattice
  8. Enumeration degrees and non-metrizable topology (with K. M. Ng, and A. Pauly)
    submitted, written in September 2017, 103 pages. [arXiv]
    Category: topological aspects of computability theory, degree theory

Publications

  1. 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
  2. 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
  3. Topological reducibilities for discontinuous functions and their structures
    to appear in Israel Journal of Mathematics, 37 pages. [arXiv]
    Category: descriptive set theory, computability theory
  4. Enumerating classes of effective quasi-Polish spaces (with M. de Brecht and V. Selivanov)
    In Proceedings of CiE 2022, Lecture Notes in Computer Science (2022), pp. 88-102. [doi]
    Category: computable topology
  5. 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
  6. 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
  7. 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
  8. 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
  9. The Brouwer invariance theorems in reverse mathematics
    Forum of Mathematics, Sigma, 8 (2020), Paper No. e51, 12 pages. [arXiv] [doi]
    Category: reverse mathematics
  10. 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
  11. 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
  12. 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
  13. 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
  14. 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
  15. 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
  16. 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
  17. 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
  18. 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
  19. 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
  20. 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
  21. 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
  22. Comparing the Medvedev and Turing degrees of Π01 classes
    Mathematical Structures in Computer Science, 25 (8) (2015), pp. 1649-1668. [doi]
    Category: degree theory
  23. 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
  24. 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
  25. Uniform Kurtz randomness (with K. Miyabe)
    Journal of Logic and Computation, 24 (4) (2014), pp. 863-882. [doi]
    Category: algorithmic randomness
  26. 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
  27. 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
  28. 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
  29. 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
  30. Incomputability of simply connected planar continua
    Computability, 1 (2) (2012), pp. 131-152. [doi]
    Category: computable topology
  31. 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
  32. 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. Descriptive Set Theory / Beyond Borel Sets
    Suuri Kagaku (Mathematical Sciences Magazine) Jun. 2022 Issue, Science-Sha.
  2. Foundations of Mathematics and Computability
    Suuri Kagaku (Mathematical Sciences Magazine) Aug. 2021 Issue, Science-Sha, pp.58-64.
  3. 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.
  4. Hilbert's Tenth Problem and its Companions
    Sugaku Seminar (Math Seminar Magazine) Nov. 2020 Issue, Nippon Hyoron Sha, pp.24-26.
  5. 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.
  6. The Ackermann Function and Hilbert
    Sugaku Seminar (Math Seminar Magazine) Jul. 2019 Issue, Nippon Hyoron Sha, pp.22-27.