Details of the Researcher

PHOTO

Takako Nemoto
Section
Graduate School of Information Sciences
Job title
Associate Professor
Degree

  • 博士（理学）（東北大学）

  • 修士（理学）（東北大学）

Research History 6

  • 2020/04 - 2023/03
    Hiroshima Institute of Technology　Department of Architectural Design　Associate Professor

  • 2012/04 - 2020/03
    Japan Advanced Institute of Science and Technology　Assistant Professor

  • 2010/04 - 2012/03
    Universität Bern　Re

  • 2009/10 - 2010/03
    Japan Advanced Institute of Science and Technology　School of Information Science　Research fellow

  • 2009/04 - 2009/08
    Part-time Lecturer at Tohoku Gakuin University

  • Research fellowship at Mathematical Research Institute, Utrecht, Netherlands (2006), Research Fellow of Japan Society for the Promotion of Science(DC2)(2007), Teaching Assistant at Tohoku University(2008)

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Professional Memberships 3

  • Computability in Europe

  • the Mathematical Society of Japan

  • Association for Symbolic Logic

Research Interests 3

  • Constructive Mathematics

  • Intuitionistic Logic

  • Reverse Mathematics

Research Areas 1

  • Natural sciences / Basic mathematics /

Papers 18

  1. Choice principles characterizing the difference between König’s lemma and weak König’s lemma in constructive reverse mathematics Peer-reviewed

    Makoto Fujiwara, Takako Nemoto

    Computability　1-8　2024/04/02

    Publisher: IOS Press

    DOI： 10.3233/com-230478 　

    ISSN： 2211-3568

    eISSN： 2211-3576

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    In the context of constructive reverse mathematics, we characterize the difference between König’s lemma and weak König’s lemma by a particular fragment of the countable choice principle. Specifically, we show that König’s lemma can be decomposed into weak König’s lemma and the choice principle over a weak intuitionistic two-sorted arithmetic.

  2. Choice and independence of premise rules in intuitionistic set theory Peer-reviewed

    Emanuele Frittaion, Takako Nemoto, Michael Rathjen

    Annals of Pure and Applied Logic　174　(9)　2023/10

    Publisher: Elsevier BV

    DOI： 10.1016/j.apal.2023.103314 　

    ISSN： 0168-0072

  3. EXTENDED FRAMES AND SEPARATIONS OF LOGICAL PRINCIPLES Peer-reviewed

    MAKOTO FUJIWARA, HAJIME ISHIHARA, TAKAKO NEMOTO, NOBU-YUKI SUZUKI, KEITA YOKOYAMA

    The Bulletin of Symbolic Logic　29　(3)　1-42　2023/07/26

    Publisher: Cambridge University Press (CUP)

    DOI： 10.1017/bsl.2023.29 　

    ISSN： 1079-8986

    eISSN： 1943-5894

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    Abstract We aim at developing a systematic method of separating omniscience principles by constructing Kripke models for intuitionistic predicate logic $\mathbf {IQC}$ and first-order arithmetic $\mathbf {HA}$ from a Kripke model for intuitionistic propositional logic $\mathbf {IPC}$. To this end, we introduce the notion of an extended frame, and show that each IPC-Kripke model generates an extended frame. By using the extended frame generated by an IPC-Kripke model, we give a separation theorem of a schema from a set of schemata in $\mathbf {IQC}$ and a separation theorem of a sentence from a set of schemata in $\mathbf {HA}$. We see several examples which give us separations among omniscience principles.

  4. On the decomposition of WKL!! Invited Peer-reviewed

    Makoto Fujiwara, Takako Nemoto

    Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences　381　(2248)　2023/04/10

    Publisher: The Royal Society

    DOI： 10.1098/rsta.2022.0010 　

    ISSN： 1364-503X

    eISSN： 1471-2962

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    From the conceptual viewpoint, many mathematical propositions implicitly contain at least two kinds of principle. One is a logical principle such as the law-of-excluded-middle or De Morgan’s law. Another is a function–existence principle. For both conceptual and practical reasons, it is an interesting enterprise to calibrate how amount of logical and function–existence principles are implicit in mathematical theorems and axioms. This is the topic of constructive reverse mathematics, which specifies necessary and sufficient axioms to prove each mathematical proposition constructively. In this paper, we decompose weak König’s lemma with a uniqueness hypothesis by Moschovakis, into logical and function–existence principles in a recent framework of constructive reverse mathematics. This article is part of the theme issue ‘Modern perspectives in Proof Theory’.

  5. Varieties of the Weak Kőnig Lemma and the Disjunctive Dependent Choice Peer-reviewed

    Josef Berger, Hajime Ishihara, Takako Nemoto

    Mathematics for Computation (M4C)　143-164　2023/04/02

    Publisher: WORLD SCIENTIFIC

    DOI： 10.1142/9789811245220_0006 　

  6. On the independence of premiss axiom and rule Peer-reviewed

    Hajime Ishihara, Takako Nemoto

    Archive for Mathematical Logic　59　(7-8)　793-815　2020/11

    Publisher: Springer Science and Business Media LLC

    DOI： 10.1007/s00153-019-00707-5 　

    ISSN： 0933-5846

    eISSN： 1432-0665

  7. Finite sets and infinite sets in weak intuitionistic arithmetic Peer-reviewed

    Takako Nemoto

    Archive for Mathematical Logic　59　(5-6)　607-657　2020/08/01

    Publisher: Springer

    DOI： 10.1007/s00153-019-00704-8 　

    ISSN： 1432-0665 0933-5846

  8. Equivalents of the finitary non-deterministic inductive definitions Peer-reviewed

    Ayana Hirata, Hajime Ishihara, Tatsuji Kawai, Takako Nemoto

    Annals of Pure and Applied Logic　170　(10)　1256-1272　2019/10

    Publisher: Elsevier BV

    DOI： 10.1016/j.apal.2019.05.005 　

    ISSN： 0168-0072

  9. The Monotone Completeness Theorem in Constructive Reverse Mathematics Peer-reviewed

    Hajime Ishihara, Takako Nemoto

    Mathesis Universalis, Computability and Proof　101-112　2019

    Publisher: Springer International Publishing

    DOI： 10.1007/978-3-030-20447-1_8 　

  10. The binary expansion and the intermediate value theorem in constructive reverse mathematics Peer-reviewed

    Josef Berger, Hajime Ishihara, Takayuki Kihara, Takako Nemoto

    Archive for Mathematical Logic　58　(1-2)　1-15　2018/05/10

    Publisher: Springer New York LLC

    DOI： 10.1007/s00153-018-0627-2 　

    ISSN： 1432-0665 0933-5846

  11. A note on the independence of premiss rule Peer-reviewed

    Hajime Ishihara, Takako Nemoto

    MATHEMATICAL LOGIC QUARTERLY　62　(1-2)　72-76　2016/02

    DOI： 10.1002/malq.201500032 　

    ISSN： 0942-5616

    eISSN： 1521-3870

  12. Non-Deterministic Inductive Definitions and Fullness Peer-reviewed

    Hajime Ishihara, Takako Nemoto

    CONCEPTS OF PROOF IN MATHEMATICS, PHILOSOPHY, AND COMPUTER SCIENCE　6　163-170　2016

    ISSN： 2198-235X

  13. Some principles weaker than Markov's principle Peer-reviewed

    Makoto Fujiwara, Hajime Ishihara, Takako Nemoto

    ARCHIVE FOR MATHEMATICAL LOGIC　54　(7-8)　861-870　2015/11

    DOI： 10.1007/s00153-015-0444-9 　

    ISSN： 0933-5846

    eISSN： 1432-0665

  14. Generalized geometric theories and set-generated classes Peer-reviewed

    Peter Aczel, Hajime Ishihara, Takako Nemoto, Yasushi Sangu

    MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE　25　(7)　1466-1483　2015/10

    DOI： 10.1017/S0960129513000236 　

    ISSN： 0960-1295

    eISSN： 1469-8072

  15. Weak weak Konig's lemma in constructive reverse mathematics Peer-reviewed

    Takako Nemoto

    PROCEEDINGS OF THE 10TH ASIAN LOGIC CONFERENCE　263-270　2010

  16. Determinacy of Wadge classes and subsystems of second order arithmetic Peer-reviewed

    Takako Nemoto

    MATHEMATICAL LOGIC QUARTERLY　55　(2)　154-176　2009/04

    DOI： 10.1002/malq.200710081 　

    ISSN： 0942-5616

  17. Complete determinacy and subsystems of second order arithmetic Peer-reviewed

    Takako Nemoto

    LOGIC AND THEORY OF ALGORITHMS　5028　457-466　2008

    DOI： 10.1007/978-3-540-69407-6_49 　

    ISSN： 0302-9743

  18. Infinite games in the Cantor space and subsystems of second order arithmetic Peer-reviewed

    Takako Nemoto, MedYahya Ould MedSalem, Kazuyuki Tanaka

    MATHEMATICAL LOGIC QUARTERLY　53　(3)　226-236　2007

    DOI： 10.1002/malq.200610041 　

    ISSN： 0942-5616

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Presentations 20

  1. Computability theory over intuitionistic logic Invited

    Takako Nemoto

    Logic Colloquium 2024, Special Session of Proof Theory　2024/06/27

  2. Recent results in constructive reverse mathematics Invited

    Takako Nemoto

    Continuity, Computability, Constructivity From Logic to Algorithms　2023/09

  3. De Morgan’s law and related principles in constructive reverse mathematics

    Takako Nemoto

    Constructive Mathematics: Foundation and Practice　2023/06

  4. On the decomposition of WKL!! Invited

    Takako Nemoto

    Type Theory, Constructive Mathematics and Geometric Logic　2023/05

  5. Reverse mathematics over intuitionistic logic Invited

    Takako Nemoto

    HaPoC Satel- lite Workshop, Computability in Europe 2021　2021/07

  6. Some properties of function spaces in reverse mathematics International-presentation Invited

    Takako Nemoto

    Das Kontinuum – 100 years later　2018/09

  7. Finite sets and infinite sets in weak intuitionistic arithmetic International-presentation Invited

    Takako Nemoto

    Chinese Logic annual meeting　2018/05

  8. Finite sets and infinite sets in constructive reverse mathematics International-presentation Invited

    Takako Nemoto

    SotFoM4: Reverse Mathematics　2017/10

  9. Recursion theory in constructive mathematics International-presentation Invited

    Takako Nemoto

    Asian Logic Conference　2017/07

  10. Intermediate value theorem and WKL for convex tree International-presentation

    Takako Nemoto

    Interval Analysis and Constructive Mathematics　2016/11

  11. Finitistically constructive Zermelo-Fraenkel set theory International-presentation Invited

    Takako Nemoto

    Operations, Sets, and Types　2016/04

  12. 二階算術における無限ゲームの決定性 Invited

    根元 多佳子

    日本数学会秋季総合分科会　2015/09/13

  13. Determinacy of Infinite Games and Reverse Mathematics: Complexity of Winning Strategies International-presentation Invited

    Takako Nemoto

    Special session of Reverse Mathematics, Computability in Europe 2015　2015/06/29

  14. A marriage of Brouwer's intuitionism and Hilbert's finitism International-presentation

    Takako Nemoto

    JAIST Logic Workshop Series 2015, Constructivism and Computability　2015/03/02

  15. A marriage of Brouwer's intuitionism and Hilbert's finitism International-presentation

    Takako Nemoto

    Fifth Workshop on Formal Topology: Spreads and Choice Sequences, Stockholm, Sweden　2015

  16. Ramified Analysis Revisited: A Refinement of Determinacy Hierarchy International-presentation Invited

    Takako Nemoto

    Proof 2013　2013/09/09

  17. Making a detour via intuitionistic theories – Embedding set theories into systems of explicit mathematics International-presentation Invited

    Takako Nemoto

    Constructive Mathematics: Foundations and Practice　2013/06/24

  18. The proof theoretic strengths of determinacy between \Sigma^0_1 and \Delta^0_2 International-presentation

    Takako Nemoto

    Logic Colloquium 2012　2012/07/12

  19. A system of explicit mathematics and $\Pi_3$ reflection

    T. Nemoto

    Logic Colloquium 2011　2011/07

  20. Determinacy and $\Pi^1_1$ transfinite recursion along $\omega$ International-presentation

    T. Nemoto

    8th Panhellenic Logic Symposium　2011/07

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Research Projects 4

  1. Constructive reverse mathematics and computational content of mathematical theorems

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Fund for the Promotion of Joint International Research (Fostering Joint International Research (B))

    Institution: Japan Advanced Institute of Science and Technology

    2021/10/07 - 2026/03/31

  2. Computability theory on intuitionistic logic and its application to constructive reverse mathematics

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (C)

    2018/04/01 - 2023/03/31

  3. Phase transitions of provability and supercritical propositions of reverse mathematics

    Tanaka Kazuyuki

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Scientific Research (B)

    Institution: Tohoku University

    2015/04/01 - 2020/03/31

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    The purpose of this study is to obtain multidimensional perspectives on the dynamism of "proof" by elucidating new incompleteness phenomena in the fundations of mathematics, e.g. the phase transition between provability and unprovability induced by parameters inserted in theorems, and supercritical propositions such as the determinacy of infinite games which cannot be proved by ordinary axioms. During the first half of the plan, we proceeded the research in five sub-themes. In the latter half, we rearranged into the following three sub-themes and obtained remarkable results. (1) Reverse mathematics and non-standard methods. (2) Open game and Weihrauch degrees. (3) Query complexity of random decision trees.

  4. Construction of an interpretation between systems of applicative theory and set theory

    TAKAKO Nemoto

    Offer Organization: Japan Society for the Promotion of Science

    System: Grants-in-Aid for Scientific Research

    Category: Grant-in-Aid for Research Activity Start-up

    Institution: Japan Advanced Institute of Science and Technology

    2012/08/31 - 2014/03/31

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    We gave an interpretation from set theory, whoes basic objects are sets, into applicative theory, whoes basic objects are operators and natural numbers, by modefing the interpretation method from set theory into type theory, proposed by P. Aczel. It turned out that set theories which can be interpreted by this new method is defferent from ordinal set theory in the following sense: 1. They allows the existtence of universal set, namely, the set of ALL set; 2. They does not allow rather weak set comperehension axioms. We have constructed an appropreate set theory which can be interpreted by this method in the sense of the proof theoretic strength.

Teaching Experience 4

  1. Mathematical Logic(E)　JAIST

  2. Fundamentals of Logic and Mathematics　JAIST

  3. 数理論理学(E)　北陸先端科学技術大学院大学

  4. 基礎論理数学　北陸先端科学技術大学院大学