- On a metric generalization of the tt-degrees and effective dimension theory
preprint written in March 2018, 34 pages.
- Searching for an analogue of ATR0 in the Weihrauch lattice (with A. Marcone, and A. Pauly)
preprint, 36 pages.
- Ordinal ranks on the Baire and non-Baire class functions
preprint written in March 2017, 22 pages.
- Enumeration degrees and non-metrizable topology (with S. Lempp, K. M. Ng, and A. Pauly)
preprint written in September 2017, 92 pages.
- On the structure of the Wadge degrees of BQO-valued Borel functions (with A. Montalbán)
submitted in May 2017, 36 pages. [arXiv]
- Turing degrees in Polish spaces and decomposability of Borel functions (with V. Gregoriades and K. M. Ng)
submitted in May 2016, 42 pages. [arXiv]
- Point degree spectra of represented spaces (with A. Pauly)
first submitted in June 2015, 36 pages. [arXiv]
- The binary expansion and the intermediate value theorem in constructive reverse mathematics (with J. Berger, H. Ishihara and T. Nemoto)
first submitted in December 2015, 18 pages.
- The uniform Martin's conjecture for many-one degrees (with A. Montalbán)
to appear in Transactions of the American Mathematical Society, 20 pages. [arXiv]
- Computability of subsets of metric spaces (with Z. Iljazović)
accepted, 40 pages.
- Borel-piecewise continuous reducibility for uniformization problems
Logical Methods in Computer Science 12 (4) (2016), pp. 1-35. [arXiv] [doi]
- Higher randomness and lim-sup forcing within and beyond hyperarithmetic
Sets and Computations, Lecture Notes Series, IMS, NUS 33 (2016), pp. 117-155.
- 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]
- 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 Pi-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 $\forall\exists$-theory of the effectively closed Medvedev degrees is decidable (with Joshua A. Cole)
Archive for Mathematical Logic 49 (2010), pp. 1-16. [doi]
- 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.
- Iterative use of the convex choice principle
A draft in Jan. 2016.
- 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.
- Null additivity in the theory of algorithmic randomness (with K. Miyabe)
- Notes on $\forall\exists!$-conservation (with Wei Wang)
- Wadge-like classifications of real-valued functions
- De Groot duality in computability theory
- Topological aspects of enumeration degrees
- The uniform Martin conjecture and Wadge degrees
- Degrees of unsolvability in topological spaces with countable cs-networks
- The second-level Borel isomorphism problem: An encounter of recursion theory and infinite dimensional topology
- An application of classical recursion theory to descriptive set theory via computable analysis
- Counterexamples in computable continuum theory
Publications in Japanese
- 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.
- 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.
- Computability theory of continua (in Japanese)
Formal Systems and Computability Theory, RIMS Kokyuroku (proceedings), Kyoto University 1729 (2011), pp. 48-66.
- 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.