## Preprints

*Lawvere-Tierney topologies for computability theorists*

preprint, 35 pages. [arXiv]

*Around the Wadge rank $\omega_2$*

preprint, 29 pages.

*A syntactic approach to Borel functions: Some extensions of Louveau's theorem*(with K. Sasaki)

submitted, 31 pages. [arXiv]

*Degree spectra of homeomorphism types of Polish spaces*(with M. Hoyrup, and V. Selivanov)

submitted, 30 pages. [arXiv]

*Degrees of incomputability, realizability and constructive reverse mathematics*

preprint, 34 pages. [arXiv]

*Wadge-like degrees of Borel bqo-valued functions*(with V. Selivanov)

submitted, 18 pages. [arXiv]

*Convex choice, finite choice, and sorting*(with A. Pauly)

submitted, 23 pages. [arXiv]*Topological reducibilities for discontinuous functions and their structures*

submitted, 22 pages. [arXiv]*Enumeration degrees and non-metrizable topology*(with K. M. Ng, and A. Pauly)

submitted, 103 pages. [arXiv]*Point degree spectra of represented spaces*(with A. Pauly)

submitted, 36 pages. [arXiv]

## Publications

*A comparison of various analytic choice principles*(with P.-E. Anglès d'Auriac)

to appear in Journal of Symbolic Logic, 26 pages. [arXiv]*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]*Searching for an analogue of ATR*(with A. Marcone, and A. Pauly)_{0}in the Weihrauch lattice

Journal of Symbolic Logic**85**(2020), no. 3, 1006–1043. [arXiv] [doi]*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]*The Brouwer invariance theorems in reverse mathematics*

Forum of Mathematics, Sigma**8**(2020), Paper No. e51, 12 pages. [arXiv] [doi]*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]*On a metric generalization of the tt-degrees and effective dimension theory*

Journal of Symbolic Logic**84**(2) (2019), pp. 726-749. [arXiv] [doi]*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]*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]*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]*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]*Computability of subsets of metric spaces*(with Z. Iljazović)

In Handbook of Computability and Complexity in Analysis, 40 pages.*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]*Borel-piecewise continuous reducibility for uniformization problems*

Logical Methods in Computer Science**12**(4) (2016), pp. 1-35. [arXiv] [doi]*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]*Decomposing Borel functions using the Shore-Slaman join theorem*

Fundamenta Mathematicae**230**(2015), pp. 1-13. [doi]*Unified characterizations of lowness properties via Kolmogorov complexity*(with K. Miyabe)

Archive for Mathematical Logic**54**(3-4) (2015), pp. 329-358. [doi]*Comparing the Medvedev and Turing degrees of Π*^{0}_{1}classes

Mathematical Structures in Computer Science**25**(8) (2015), pp. 1649-1668. [doi]*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]*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]*Uniform Kurtz randomness*(with K. Miyabe)

Journal of Logic and Computation**24**(4) (2014), pp. 863-882. [doi]*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]*On the strength of marriage theorems and uniformity*(with M. Fujiwara and K. Higuchi)

Mathematical Logic Quarterly**60**(3) (2014) pp. 136-153. [doi]*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]*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]*Incomputability of simply connected planar continua*

Computability**1**(2) (2012), pp. 131-152. [doi]*The ∀∃-theory of the effectively closed Medvedev degrees is decidable*(with J. A. Cole)

Archive for Mathematical Logic**49**(2010), pp. 1-16. [doi]*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

*Effective forcing with Cantor manifolds*

A draft in Feb. 2017.*A priority argument in descriptive set theory: A very detailed exposition of Semmes' proof*

First draft in 2014, Current version in Feb. 2018.*Null additivity in the theory of algorithmic randomness*(with K. Miyabe)

unpublished, 2014.*Notes on ∀∃!-conservation*(with Wei Wang)

unpublished, 2011.

## Publications in Japanese

*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.*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.*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.*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.

## Miscellaneous

*逆数学のこころ／白黒ではなく色鮮やかに*

数学セミナー 2021年2月号，日本評論社, pp.15-19.*ヒルベルトの第10問題とその仲間たち*

数学セミナー 2020年11月号，日本評論社, pp.24-26.*無限の名を呼ぶ――巨大関数をとりまく数学小史*

現代思想 2019年12月号，青土社, pp.19-28.*アッカーマン関数とヒルベルト*

数学セミナー 2019年7月号，日本評論社, pp.22-27.