## Index

[Preprints] [Publications] [Unpublished Notes] [Publications in Japanese] [Magazine Articles] |

## Preprints

*Rethinking the notion of oracle: A link between synthetic descriptive set theory and effective topos theory*

preprint, 51 pages. [arXiv]

Category: synthetic descriptive set theory, topos theory, Weihrauch lattice*Lawvere-Tierney topologies for computability theorists*

preprint, 35 pages. [arXiv]

Category: topos theory, Weihrauch lattice*On some topics around the Wadge rank ω*_{2}

preprint, 31 pages. [arXiv]

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

submitted, 31 pages. [arXiv]

Category: descriptive set theory*Degree spectra of homeomorphism types of Polish spaces*(with M. Hoyrup, and V. Selivanov)

submitted in April 2020, 30 pages. [arXiv]

Category: computable topology*Degrees of incomputability, realizability and constructive reverse mathematics*

in preparation, 34 pages. [arXiv]

Category: constructive reverse mathematics, Weihrauch lattice*Convex choice, finite choice, and sorting*(with A. Pauly)

submitted in May 2019, 23 pages. [arXiv]

Category: Weihrauch lattice*Enumeration degrees and non-metrizable topology*(with K. M. Ng, and A. Pauly)

submitted, written in September 2017, 103 pages. [arXiv]

Category: topological aspects of computability theory, degree theory

## Publications

*Point degree spectra of represented spaces*(with A. Pauly)

**Forum of Mathematics, Sigma**, 10 (2022), e31, 1-27. [arXiv] [doi]

Category: descriptive set theory, topological dimension theory, application of computability theory*Wadge-like degrees of Borel bqo-valued functions*(with V. Selivanov)

**Proceedings of the American Mathematical Society**, 150 (2022), no. 9, 3989-4003. [arXiv] [doi]

Category: descriptive set theory, BQO theory*Topological reducibilities for discontinuous functions and their structures*

to appear in**Israel Journal of Mathematics**, 37 pages. [arXiv]

Category: descriptive set theory, computability theory*Enumerating classes of effective quasi-Polish spaces*(with M. de Brecht and V. Selivanov)

In**Proceedings of CiE 2022**, Lecture Notes in Computer Science (2022), pp. 88-102. [doi]

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

**Journal of Symbolic Logic**, 86 (2021), no. 4, 1452-1485. [arXiv] [doi]

Category: Weihrauch lattice*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]

Category: descriptive set theory, application of computability theory*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]

Category: Weihrauch lattice*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]

Category: descriptive set theory*The Brouwer invariance theorems in reverse mathematics*

**Forum of Mathematics, Sigma**, 8 (2020), Paper No. e51, 12 pages. [arXiv] [doi]

Category: reverse mathematics*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]

Category: computable topology*On a metric generalization of the tt-degrees and effective dimension theory*

**Journal of Symbolic Logic**, 84 (2) (2019), pp. 726-749. [arXiv] [doi]

Category: topological aspects of computability theory, Kolmogorov complexity*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]

Category: descriptive set theory, BQO theory, application of computability theory*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]

Category: Weihrauch lattice*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]

Category: constructive reverse mathematics*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]

Category: computability theory, degree theory, BQO theory*Computability of subsets of metric spaces*(with Z. Iljazović)

In: Brattka V., Hertling P. (eds)**Handbook of Computability and Complexity in Analysis**, Theory and Applications of Computability (In cooperation with the association Computability in Europe). Springer, Cham., pp. 29-69. [doi]

Category: computable analysis*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]

Category: higher computability theory, higher randomness*Borel-piecewise continuous reducibility for uniformization problems*

**Logical Methods in Computer Science**, 12 (4) (2016), pp. 1-35. [arXiv] [doi]

Category: discontinuous functions, computable analysis*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]

Category: Weihrauch lattice*Decomposing Borel functions using the Shore-Slaman join theorem*

**Fundamenta Mathematicae**, 230 (2015), pp. 1-13. [doi]

Category: descriptive set theory, application of computability theory*Unified characterizations of lowness properties via Kolmogorov complexity*(with K. Miyabe)

**Archive for Mathematical Logic**, 54 (3-4) (2015), pp. 329-358. [doi]

Category: algorithmic randomness*Comparing the Medvedev and Turing degrees of Π*^{0}_{1}classes

**Mathematical Structures in Computer Science**, 25 (8) (2015), pp. 1649-1668. [doi]

Category: degree theory*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]

Category: degree theory, Weihrauch lattice*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]

Category: computability theory, discontinuous functions*Uniform Kurtz randomness*(with K. Miyabe)

**Journal of Logic and Computation**, 24 (4) (2014), pp. 863-882. [doi]

Category: algorithmic randomness*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]

Category: computable measure theory*On the strength of marriage theorems and uniformity*(with M. Fujiwara and K. Higuchi)

**Mathematical Logic Quarterly**, 60 (3) (2014) pp. 136-153. [doi]

Category: reverse mathematics*Effective strong nullness and effectively closed sets*(with K. Higuchi)

In**Procedings of CiE 2012**, Lecture Notes in Computer Science, 7318 (2012), pp. 304-313. [doi]

Category: degree theory, computable measure theory*A hierarchy of immunity and density for sets of reals*

In**Procedings of CiE 2012**, Lecture Notes in Computer Science, 7318 (2012), pp. 385-395. [doi]

Category: degree theory*Incomputability of simply connected planar continua*

**Computability**, 1 (2) (2012), pp. 131-152. [doi]

Category: computable topology*The ∀∃-theory of the effectively closed Medvedev degrees is decidable*(with J. A. Cole)

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

Category: degree theory*Immunity and non-cupping for closed sets*(with D. Cenzer, R. Weber and G. Wu)

**Tbilisi Mathematical Journal**, 2 (2009), pp. 77-94.

Category: degree theory

## 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, Second draft in 2016, Current version in Feb. 2018.

Category: descriptive set theory, application of computability theory*Null additivity in the theory of algorithmic randomness*(with K. Miyabe)

written in 2014, submitted to MLQ, rejected in Feb. 2016.

Category: generalized computability theory, algorithmic randomness*Notes on ∀∃!-conservation*(with Wei Wang)

unpublished, 2011.

Category: reverse mathematics

## 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.

Category: descriptive set theory, application of computability theory*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.

Category: cardinal invariants, algorithmic randomness*Computability theory of continua (in Japanese)*

Formal Systems and Computability Theory, RIMS Kokyuroku (proceedings), Kyoto University**1729**(2011), pp. 48-66.

Category: computable topology*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.

Category: reverse mathematics, reverse recursion theory

## Magazine Articles (for the General Public, written in Japanese)

*Descriptive Set Theory / Beyond Borel Sets*

Suuri Kagaku (Mathematical Sciences Magazine) Jun. 2022 Issue, Science-Sha.*Foundations of Mathematics and Computability*

Suuri Kagaku (Mathematical Sciences Magazine) Aug. 2021 Issue, Science-Sha, pp.58-64.*The Heart of Reverse Mathematics / Don't be Monochrome, Be Colorful*

Sugaku Seminar (Math Seminar Magazine) Feb. 2021 Issue, Nippon Hyoron Sha, pp.15-19.*Hilbert's Tenth Problem and its Companions*

Sugaku Seminar (Math Seminar Magazine) Nov. 2020 Issue, Nippon Hyoron Sha, pp.24-26.*Calling the Name of Infinity: A Short History of Mathematics Surrounding Fast Growing Functions*

Gendai Siso (Contemporary Philosophy) Dec. 2019 Issue, Seido Sha, pp.19-28.*The Ackermann Function and Hilbert*

Sugaku Seminar (Math Seminar Magazine) Jul. 2019 Issue, Nippon Hyoron Sha, pp.22-27.