## Preprints

*On a metric generalization of the tt-degrees and effective dimension theory*

submitted in March 2018, 34 pages. [arXiv]*Searching for an analogue of ATR*(with A. Marcone, and A. Pauly)_{0}in the Weihrauch lattice

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.*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]

## Publications

*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]*The uniform Martin's conjecture for many-one degrees*(with A. Montalbán)

to appear in Transactions of the American Mathematical Society, 20 pages. [arXiv] [doi]*Computability of subsets of metric spaces*(with Z. Iljazović)

accepted, 40 pages.*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]*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. [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 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.

## Unpublished Notes

*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)

unpublised, 2014.*Notes on $\forall\exists!$-conservation*(with Wei Wang)

unpublished, 2011.

## Selected Slides

*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.