Index
[Preprints] [Publications] [Unpublished Notes] [Publications in Japanese] [Magazine Articles] |
Preprints
- The fourth level of the realizability-theoretic arithmetical hierarchy (with G. Glowacki and K. Takayanagi)
in preparation.
Category: degree theory, realizability - The arithmetical hierarchy: A realizability-theoretic perspective
in preparation, 43 pages. [arXiv]
Category: degree theory, realizability - Church's thesis in subtoposes of the effective topos (with K. M. Ng)
in preparation.
Category: constructive reverse mathematics, degree theory, realizability, topos - The subTuring degrees (with K. M. Ng)
in preparation, 22 pages. [arXiv]
Category: degree theory, realizability - Degree structures of function spaces over unusual ground types (with K. M. Ng)
in preparation, 56 pages.
Category: degree theory, computable topology - De Groot-like duality for represented spaces (with A. Pauly)
in preparation, 35 pages.
Category: computable topology, synthetic topology - Rethinking the notion of oracle: A prequel to Lawvere-Tierney topologies for computability theorists
submitted, 57 pages. [arXiv]
Category: synthetic descriptive set theory, topos theory, Weihrauch lattice - On some topics around the Wadge rank ω2
submitted, 31 pages. [arXiv]
Category: descriptive set theory - 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
Publications
- Many-one reducibility with realizability
to appear in Journal of Symbolic Logic, 36 pages. [arXiv]
Category: degree theory, realizability - Enumeration degrees and non-metrizable topology (with K. M. Ng, and A. Pauly)
to appear in Memoirs of the American Mathematical Society. [arXiv]
Category: topological aspects of computability theory, degree theory - On the metric temporal logic for continuous stochastic processes (with M. Ikeda and Y. Yamagata)
Logical Methods in Computer Science, 20 (2024), Issue 2, pp. 14:1-14:35. [arXiv] [doi]
Category: temporal logic - Ideal presentations and numberings of some classes of effective quasi-Polish spaces (with M. de Brecht and V. Selivanov)
to appear in Computability. [arXiv] [doi]
Category: computable topology - Degree spectra of homeomorphism types of Polish spaces (with M. Hoyrup, and V. Selivanov)
to appear in Journal of Symbolic Logic. [arXiv] [doi]
Category: computable topology - On the main scientific achievements of Victor Selivanov (with N. Bazhenov, S. Selivanova and D. Spreen)
Computability, 12 (2023), no. 4, 301-314. [doi]
- De Groot duality for represented spaces (with A. Pauly)
In Proceedings of CiE 2023, Lecture Notes in Computer Science, 13967 (2023), 89-101. [doi]
Category: computable topology - Lawvere-Tierney topologies for computability theorists
Transactions of the American Mathematical Society, Series B, 10 (2023), 48-85. [arXiv] [doi]
Category: topos theory, Weihrauch lattice - A syntactic approach to Borel functions: Some extensions of Louveau's theorem (with K. Sasaki)
Archive for Mathematical Logic, 62 (2023), 1041-1082. [arXiv] [doi]
Category: descriptive set theory - 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
Israel Journal of Mathematics, 252 (2022), pp. 461-500. [arXiv] [doi]
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, 13359 (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 ATR0 in the Weihrauch lattice (with A. Marcone, and A. Pauly)
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 Π01 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)
- Important Sets of Lebesgue Measure Zero
Sugaku Seminar (Math Seminar Magazine) Nov. 2024 Issue, Nippon Hyoron Sha. - Rigor, Abstraction, and Development of "Computability" in Mathematics
Gendai Siso (Contemporary Philosophy) Jul. 2023 Issue, Seido Sha, pp. 51-63. - 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.