国立大学法人 名古屋大学 | 大学院情報学研究科 | 数理情報学専攻 | 数理情報基礎論講座

Preprints

  1. A comparison of various analytic choice principles (with P.-E. Anglès D'Auriac)
    submitted, 26 pages.
  2. Searching for an analogue of ATR0 in the Weihrauch lattice (with A. Marcone, and A. Pauly)
    submitted, 35 pages. [arXiv]
  3. Finite choice, convex choice and sorting (with A. Pauly)
    submitted, 17 pages.
  4. Decomposing functions of Baire class 2 on Polish spaces (with L. Ding, B. Semmes, and J. Zhao)
    submitted, 18 pages. [arXiv]
  5. On a metric generalization of the tt-degrees and effective dimension theory
    submitted, 34 pages. [arXiv]
  6. Ordinal ranks on the Baire and non-Baire class functions
    preprint, 22 pages.
  7. Enumeration degrees and non-metrizable topology (with K. M. Ng, and A. Pauly)
    preprint, 103 pages.
  8. Turing degrees in Polish spaces and decomposability of Borel functions (with V. Gregoriades and K. M. Ng)
    submitted, 42 pages. [arXiv]
  9. Point degree spectra of represented spaces (with A. Pauly)
    submitted, 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] [doi]
  2. 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]
  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 Π01 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 J. 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. A priority argument in descriptive set theory: A very detailed exposition of Semmes' proof
    First draft in 2014, Current version in Feb. 2018.
  3. Null additivity in the theory of algorithmic randomness (with K. Miyabe)
    unpublished, 2014.
  4. Notes on $\forall\exists!$-conservation (with Wei Wang)
    unpublished, 2011.

Publications in Japanese

  1. ボレル関数の分解問題への計算論の応用(アブストラクト)
    理論計算機科学の新展開, 京都大学数理解析研究所講究録 1849 (2013), pp. 32-36.
  2. 実数の集合論とランダムネス(概説)
    証明論と複雑性, 京都大学数理解析研究所講究録 1832 (2013), pp. 97-113.
  3. 連続体の計算可能性理論
    形式体系と計算理論, 京都大学数理解析研究所講究録 1729 (2011), pp. 48-66.
  4. 逆数学と逆再帰理論について
    証明論と論理・計算の構造, 京都大学数理解析研究所講究録 1635 (2009), pp. 51-59.