- 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]
- 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 ATR0 in the Weihrauch lattice (with A. Marcone, and A. Pauly)
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 Π01 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.
- 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)
- Notes on ∀∃!-conservation (with Wei Wang)
Publications in Japanese
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.
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.
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.
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.
数学セミナー 2021年2月号，日本評論社, pp.15-19.
数学セミナー 2020年11月号，日本評論社, pp.24-26.
現代思想 2019年12月号，青土社, pp.19-28.
数学セミナー 2019年7月号，日本評論社, pp.22-27.