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

Preprints

  1. On a metric generalization of the tt-degrees and effective dimension theory
    submitted in March 2018, 34 pages. [arXiv]
  2. Searching for an analogue of ATR0 in the Weihrauch lattice (with A. Marcone, and A. Pauly)
    preprint, 36 pages.
  3. Ordinal ranks on the Baire and non-Baire class functions
    preprint written in March 2017, 22 pages.
  4. Enumeration degrees and non-metrizable topology (with S. Lempp, K. M. Ng, and A. Pauly)
    preprint written in September 2017, 92 pages.
  5. Turing degrees in Polish spaces and decomposability of Borel functions (with V. Gregoriades and K. M. Ng)
    submitted in May 2016, 42 pages. [arXiv]
  6. Point degree spectra of represented spaces (with A. Pauly)
    first submitted in June 2015, 36 pages. [arXiv]

Publications

  1. On the structure of the Wadge degrees of BQO-valued Borel functions (with A. Montalbán)
    to appear in Transactions of the American Mathematical Society, 39 pages. [arXiv]
  2. The uniform Martin's conjecture for many-one degrees (with A. Montalbán)
    to appear in Transactions of the American Mathematical Society, 20 pages. [arXiv] [doi]
  3. Computability of subsets of metric spaces (with Z. Iljazović)
    accepted, 40 pages.
  4. The binary expansion and the intermediate value theorem in constructive reverse mathematics (with J. Berger, H. Ishihara and T. Nemoto)
    to appear in Archive for Mathematical Logic. [doi]
  5. Borel-piecewise continuous reducibility for uniformization problems
    Logical Methods in Computer Science 12 (4) (2016), pp. 1-35. [arXiv] [doi]
  6. Higher randomness and lim-sup forcing within and beyond hyperarithmetic
    Sets and Computations, Lecture Notes Series, IMS, NUS 33 (2016), pp. 117-155. [doi]
  7. 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]
  8. Decomposing Borel functions using the Shore-Slaman join theorem
    Fundamenta Mathematicae 230 (2015), pp. 1-13. [doi]
  9. Unified characterizations of lowness properties via Kolmogorov complexity (with K. Miyabe)
    Archive for Mathematical Logic 54 (3-4) (2015), pp. 329-358. [doi]
  10. Comparing the Medvedev and Turing degrees of Pi-0-1 classes
    Mathematical Structures in Computer Science 25 (8) (2015), pp. 1649-1668. [doi]
  11. 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]
  12. 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]
  13. Uniform Kurtz randomness (with K. Miyabe)
    Journal of Logic and Computation 24 (4) (2014), pp. 863-882. [doi]
  14. 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]
  15. On the strength of marriage theorems and uniformity (with M. Fujiwara and K. Higuchi)
    Mathematical Logic Quarterly 60 (3) (2014) pp. 136-153. [doi]
  16. 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]
  17. 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]
  18. Incomputability of simply connected planar continua
    Computability 1 (2) (2012), pp. 131-152. [doi]
  19. The $\forall\exists$-theory of the effectively closed Medvedev degrees is decidable (with Joshua A. Cole)
    Archive for Mathematical Logic 49 (2010), pp. 1-16. [doi]
  20. 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. Iterative use of the convex choice principle
    A draft in Jan. 2016.
  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 Dec. 2017.
  4. Null additivity in the theory of algorithmic randomness (with K. Miyabe)
    unpublised, 2014.
  5. Notes on $\forall\exists!$-conservation (with Wei Wang)
    unpublished, 2011.

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.
  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.
  3. Computability theory of continua (in Japanese)
    Formal Systems and Computability Theory, RIMS Kokyuroku (proceedings), Kyoto University 1729 (2011), pp. 48-66.
  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.