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

Preprints

  1. Degrees of incomputability, realizability and constructive reverse mathematics
    in preparation, 34 pages. [arXiv]
    Category: constructive reverse mathematics, Weihrauch lattice
  2. Wadge-like degrees of Borel bqo-valued functions (with V. Selivanov)
    submitted in September 2019, 18 pages. [arXiv]
    Category: descriptive set theory, BQO theory
  3. The Brouwer invariance theorems in reverse mathematics
    submitted in February 2019, 16 pages. [arXiv]
    Category: reverse mathematics
  4. Convex choice, finite choice, and sorting (with A. Pauly)
    submitted in May 2019, 23 pages. [arXiv]
    Category: Weihrauch lattice
  5. A comparison of various analytic choice principles (with P.-E. Anglès d'Auriac)
    submitted in December 2018, 26 pages. [arXiv]
    Category: Weihrauch lattice
  6. Decomposing functions of Baire class 2 on Polish spaces (with L. Ding, B. Semmes, and J. Zhao)
    submitted in August 2018, 18 pages. [arXiv]
    Category: descriptive set theory
  7. Topological reducibilities for discontinuous functions and their structures
    submitted, written in March 2017, 22 pages. [arXiv]
    Category: descriptive set theory, computability theory
  8. Enumeration degrees and non-metrizable topology (with K. M. Ng, and A. Pauly)
    preprint written in September 2017, 103 pages. [arXiv]
    Category: topological aspects of computability theory, degree theory
  9. Point degree spectra of represented spaces (with A. Pauly)
    submitted in June 2015, 36 pages. [arXiv]
    Category: descriptive set theory, topological dimension theory, application of computability theory

Publications

  1. Turing degrees in Polish spaces and decomposability of Borel functions (with V. Gregoriades and K. M. Ng)
    to appear in Journal of Mathematical Logic, 42 pages. [arXiv]
    Category: descriptive set theory, application of computability theory
  2. Searching for an analogue of ATR0 in the Weihrauch lattice (with A. Marcone, and A. Pauly)
    to appear in Journal of Symbolic Logic, 35 pages. [arXiv]
    Category: Weihrauch lattice
  3. 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
  4. 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
  5. 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
  6. 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
  7. 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
  8. Computability of subsets of metric spaces (with Z. Iljazović)
    In Handbook of Computability and Complexity in Analysis, 40 pages.
    Category: computable analysis
  9. 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
  10. 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
  11. 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
  12. 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
  13. 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
  14. Comparing the Medvedev and Turing degrees of Π01 classes
    Mathematical Structures in Computer Science, 25 (8) (2015), pp. 1649-1668. [doi]
    Category: degree theory
  15. 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
  16. 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
  17. Uniform Kurtz randomness (with K. Miyabe)
    Journal of Logic and Computation, 24 (4) (2014), pp. 863-882. [doi]
    Category: algorithmic randomness
  18. 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
  19. 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
  20. 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
  21. 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
  22. Incomputability of simply connected planar continua
    Computability, 1 (2) (2012), pp. 131-152. [doi]
    Category: computable topology
  23. 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
  24. 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

Selected Slides

  1. Wadge-like classifications of real-valued functions
  2. De Groot duality in computability theory
  3. Topological aspects of enumeration degrees
  4. The uniform Martin conjecture and Wadge degrees
  5. Degrees of unsolvability in topological spaces with countable cs-networks
  6. The second-level Borel isomorphism problem: An encounter of recursion theory and infinite dimensional topology
  7. An application of classical recursion theory to descriptive set theory via computable analysis
  8. Counterexamples in computable continuum theory

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