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Keita Yokoyama

Section

Graduate School of Science

Job title

Professor

Degree

博士（理学）（東北大学）
修士（理学）（東北大学）
学士（理学）（東京工業大学）

researchmap

https://researchmap.jp/read0145758

J-GLOBAL ID

200901043117707317

Education 3

Tohoku University

2005/04 - 2008/03
Tohoku University

2004/04 - 2005/03
Tokyo Institute of Technology　School of Science

2000/04 - 2004/03

Committee Memberships 6

日本数学会　評議員

2025/03 - Present
Annals of Pure and Applied Logic　Editor

2021/01 - Present
Association for Symbolic Logic　Council

2020/01 - 2024/12
Association for Symbolic Logic　East Asia Regional committee (chair 2021--2024)

2019/01 - 2024/12
日本数学会　雑誌数学編集委員

2020/07 - 2024/06
日本数学会　数学基礎論及び歴史分科会運営委員

2022/03 - 2024/02

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Professional Memberships 2

日本数学会
Association for Symbolic Logic

Research Interests 5

proof-theory
model theory of arithmetic
nonstandard analysis
Reverse Mathematics
second-order arithemtic

Research Areas 1

Natural sciences / Basic mathematics /

Papers 34

On the Π21 consequences of Π11-CA0

Yudai Suzuki, Keita Yokoyama

Journal of Mathematical Logic　2025/08/05

DOI： 10.1142/S0219061325500151 　
A PARAMETERIZED HALTING PROBLEM, $ \Delta _0$ TRUTH AND THE MRDP THEOREM

YIJIA CHEN, MORITZ MÜLLER, KEITA YOKOYAMA

The Journal of Symbolic Logic　2025/06

DOI： 10.1017/jsl.2024.44 　
An isomorphism theorem for models of weak König’s lemma without primitive recursion

Marta Fiori-Carones, Leszek Aleksander Kołodziejczyk, Tin Lok Wong, Keita Yokoyama

Journal of the European Mathematical Society　2024/09/20

DOI： 10.4171/jems/1522 　

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We prove that if $(M,\mathcal{X})$ and $(M,\mathcal{Y})$ are countable models of the theory $\mathrm{WKL}^*_0$ such that $\mathrm{I}\Sigma_1(A)$ fails for some $A \in \mathcal{X} \cap \mathcal{Y}$, then $(M,\mathcal{X})$ and $(M,\mathcal{Y})$ are isomorphic. As a consequence, the analytic hierarchy collapses to $\Delta^1_1$ provably in $\mathrm{WKL}^*_0 + \neg\mathrm{I}\Sigma^0_1$, and $\mathrm{WKL}$ is the strongest $\Pi^1_2$ statement that is $\Pi^1_1$-conservative over $\mathrm{RCA}^*_0 + \neg\mathrm{I}\Sigma^0_1$. Applying our results to the $\Delta^0_n$-definable sets in models of $\mathrm{RCA}^*_0 + \mathrm{B}\Sigma^0_n + \neg\mathrm{I}\Sigma^0_n$ that also satisfy an appropriate relativization of Weak K\"onig's Lemma, we prove that for each $n \ge 1$, the set of $\Pi^1_2$ sentences that are $\Pi^1_1$-conservative over $\mathrm{RCA}^*_0 + \mathrm{B}\Sigma^0_n + \neg\mathrm{I}\Sigma^0_n$ is c.e. In contrast, we prove that the set of $\Pi^1_2$ sentences that are $\Pi^1_1$-conservative over $\mathrm{RCA}^*_0 + \mathrm{B}\Sigma^0_n$ is $\Pi_2$-complete. This answers a question of Towsner. We also show that $\mathrm{RCA}_0 + \mathrm{RT}^2_2$ is $\Pi^1_1$-conservative over $\mathrm{B}\Sigma^0_2$ if and only if it is conservative over $\mathrm{B}\Sigma^0_2$ with respect to $\forall \Pi^0_5$ sentences.
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.
How strong is Ramsey’s theorem if infinity can be weak? Peer-reviewed

Leszek Aleksander Kołodziejczyk, Katarzyna W. Kowalik, Keita Yokoyama

The Journal of Symbolic Logic　1-21　2022/06/14
Publisher: Cambridge University Press (CUP)
DOI： 10.1017/jsl.2022.46 　

ISSN： 0022-4812

eISSN： 1943-5886
THE REVERSE MATHEMATICS OF THEOREMS OF JORDAN AND LEBESGUE Peer-reviewed

ANDR{\'{E } } NIES, MARCUS A. TRIPLETT, KEITA YOKOYAMA

The Journal of Symbolic Logic　86　(4)　1657-1675　2021/12
Publisher: Cambridge University Press ({CUP})
DOI： 10.1017/jsl.2021.16 　

ISSN： 0022-4812 1943-5886

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accepted for publication
In Search of the First-Order Part of Ramsey’s Theorem for Pairs Invited Peer-reviewed

Leszek Aleksander Kołodziejczyk, Keita Yokoyama

Lecture Notes in Computer Science　12813　297-307　2021/07
Publisher: Springer International Publishing
DOI： 10.1007/978-3-030-80049-9_27 　

ISSN： 0302-9743

eISSN： 1611-3349
Ekeland’s variational principle in weak and strong systems of arithmetic Peer-reviewed

David Fernández-Duque, Paul Shafer, Keita Yokoyama

Selecta Mathematica　26　(5)　2020/11
Publisher: Springer Science and Business Media {LLC}
DOI： 10.1007/s00029-020-00597-z 　

ISSN： 1022-1824

eISSN： 1420-9020

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<title>Abstract</title>We analyze Ekeland’s variational principle in the context of reverse mathematics. We find that that the full variational principle is equivalent to <inline-formula><alternatives><tex-math>$$\Pi ^1_1\text{- }\mathsf {CA}_0$$</tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>Π</mml:mi> <mml:mn>1</mml:mn> <mml:mn>1</mml:mn> </mml:msubsup> <mml:mtext>-</mml:mtext> <mml:mspace /> <mml:msub> <mml:mi>CA</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> </mml:math></alternatives></inline-formula>, a strong theory of second-order arithmetic, while natural restrictions (e.g. to compact spaces or to continuous functions) yield statements equivalent to weak König’s lemma (<inline-formula><alternatives><tex-math>$$\mathsf {WKL}_0$$</tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>WKL</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math></alternatives></inline-formula>) and to arithmetical comprehension (<inline-formula><alternatives><tex-math>$$\mathsf {ACA}_0$$</tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ACA</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math></alternatives></inline-formula>). We also find that the localized version of Ekeland’s variational principle is equivalent to <inline-formula><alternatives><tex-math>$$\Pi ^1_1\text{- }\mathsf {CA}_0$$</tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>Π</mml:mi> <mml:mn>1</mml:mn> <mml:mn>1</mml:mn> </mml:msubsup> <mml:mtext>-</mml:mtext> <mml:mspace /> <mml:msub> <mml:mi>CA</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> </mml:math></alternatives></inline-formula>, even when restricted to continuous functions. This is a rare example of a statement about continuous functions having great logical strength.
Some upper bounds on ordinal-valued Ramsey numbers for colourings of pairs Peer-reviewed

Leszek Aleksander Kołodziejczyk, Keita Yokoyama

Selecta Mathematica　26　(4)　2020/09
Publisher: Springer Science and Business Media LLC
DOI： 10.1007/s00029-020-00577-3 　

ISSN： 1022-1824

eISSN： 1420-9020
Ramsey's theorem for pairs, collection, and proof size

Leszek Aleksander Kołodziejczyk, Tin Lok Wong, Keita Yokoyama

2020

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preprint
Combinatorial principles equivalent to weak induction Peer-reviewed

Davis, C., Hirschfeldt, D.R., Hirst, J., Pardo, J., Pauly, A., Yokoyama, K.

Computability　9　(3-4)　1-12　2020
Publisher: IOS Press
DOI： 10.3233/COM-180244 　

ISSN： 2211-3576 2211-3568

eISSN： 2211-3576
The strength of SCT soundness Peer-reviewed

Frittaion, E., Pelupessy, F., Steila, S., Yokoyama, K.

Journal of Logic and Computation　28　(6)　2018

DOI： 10.1093/logcom/exy003 　

ISSN： 1465-363X 0955-792X
Erdos-Moser and ISigma_2

Henry Towsner, Keita Yokoyama

2018

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preprint
The strength of ramsey's theorem for pairs and arbitrarily many colors Peer-reviewed

Slaman, T.A., Yokoyama, K.

Journal of Symbolic Logic　83　(4)　1610-1617　2018

DOI： 10.1017/jsl.2018.19 　

ISSN： 0022-4812
A parameterized halting problem, the linear time hierarchy, and the MRDP theorem Peer-reviewed

Yijia Chen, Moritz Müller, Keita Yokoyama

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science　235-244　2018

DOI： 10.1145/3209108.3209155 　
The proof-theoretic strength of Ramsey's theorem for pairs and two colors Peer-reviewed

Patey, L., Yokoyama, K.

Advances in Mathematics　330　1034-1070　2018

DOI： 10.1016/j.aim.2018.03.035 　

ISSN： 1090-2082 0001-8708
The strength of the sct criterion Peer-reviewed

Emanuele Frittaion, Silvia Steila, Keita Yokoyama

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)　10185　260-273　2017
Publisher: Springer Verlag
DOI： 10.1007/978-3-319-55911-7_19 　

ISSN： 1611-3349 0302-9743
Reverse mathematical bounds for the Termination Theorem Peer-reviewed

Silvia Steila, Keita Yokoyama

ANNALS OF PURE AND APPLIED LOGIC　167　(12)　1213-1241　2016/12

DOI： 10.1016/j.apal.2016.06.001 　

ISSN： 0168-0072

eISSN： 1873-2461
On principles between Sigma(1)- and Sigma(2)-induction, and monotone enumerations Peer-reviewed

Alexander P. Kreuzer, Keita Yokoyama

JOURNAL OF MATHEMATICAL LOGIC　16　(1)　2016/06

DOI： 10.1142/S0219061316500045 　

ISSN： 0219-0613

eISSN： 1793-6691
Notes on various versions of Friedman's self-embedding theorem Peer-reviewed

Keita Yokoyama

Studies in Weak Arithmetics　3　231-241　2016
Categorical characterizations of the natural numbers require primitive recursion Peer-reviewed

Leszek Aleksander Kolodziejczyk, Keita Yokoyama

ANNALS OF PURE AND APPLIED LOGIC　166　(2)　219-231　2015/02

DOI： 10.1016/j.apal.2014.10.003 　

ISSN： 0168-0072

eISSN： 1873-2461
Propagation of partial randomness Peer-reviewed

Kojiro Higuchi, W. M. Philip Hudelson, Stephen G. Simpson, Keita Yokoyama

ANNALS OF PURE AND APPLIED LOGIC　165　(2)　742-758　2014/02

DOI： 10.1016/j.apal.2013.10.006 　

ISSN： 0168-0072

eISSN： 1873-2461
Nonstandard second-order arithmetic and Riemann's mapping theorem Peer-reviewed

Yoshihiro Horihata, Keita Yokoyama

ANNALS OF PURE AND APPLIED LOGIC　165　(2)　520-551　2014/02

DOI： 10.1016/j.apal.2013.06.022 　

ISSN： 0168-0072

eISSN： 1873-2461
On the Ramseyan factorization theorem Peer-reviewed

Shota Murakami, Takeshi Yamazaki, Keita Yokoyama

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)　8493　324-332　2014
Publisher: Springer Verlag
DOI： 10.1007/978-3-319-08019-2_33 　

ISSN： 1611-3349 0302-9743
Reverse mathematics and Peano categoricity Peer-reviewed

Stephen G. Simpson, Keita Yokoyama

ANNALS OF PURE AND APPLIED LOGIC　164　(3)　284-293　2013/03

DOI： 10.1016/j.apal.2012.10.014 　

ISSN： 0168-0072

eISSN： 1873-2461
On the strength of Ramsey's theorem without Σ1-induction Peer-reviewed

Keita Yokoyama

Mathematical Logic Quarterly　59　(1-2)　108-111　2013/02

DOI： 10.1002/malq.201200047 　

ISSN： 0942-5616 1521-3870
A note on the sequential version of Π2 1 statements Peer-reviewed

Makoto Fujiwara, Keita Yokoyama

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)　7921　171-180　2013

DOI： 10.1007/978-3-642-39053-1_20 　

ISSN： 0302-9743 1611-3349
The Dirac delta function in two settings of Reverse Mathematics Peer-reviewed

Sam Sanders, Keita Yokoyama

ARCHIVE FOR MATHEMATICAL LOGIC　51　(1-2)　99-121　2012/02

DOI： 10.1007/s00153-011-0256-5 　

ISSN： 1432-0665
A Nonstandard Counterpart of WWKL Peer-reviewed

Stephen G. Simpson, Keita Yokoyama

NOTRE DAME JOURNAL OF FORMAL LOGIC　52　(3)　229-243　2011

DOI： 10.1215/00294527-1435429 　

ISSN： 0029-4527
FORMALIZING NON STANDARD ARGUMENTS IN SECOND ORDER ARITHMETIC Peer-reviewed

Keita Yokoyama

JOURNAL OF SYMBOLIC LOGIC　75　(4)　1199-1210　2010/12

ISSN： 0022-4812

eISSN： 1943-5886
On Pi^1_1 conservativity of Pi^1_2 theories in second order arithmetic Peer-reviewed

Keita Yokoyama

Proceedings of the 10th Asian Logic Conference, World Scientific　375-386　2008
The Jordan curve theorem and the Schonflies theorem in weak second-order arithmetic Peer-reviewed

Nobuyuki Sakamoto, Keita Yokoyama

ARCHIVE FOR MATHEMATICAL LOGIC　46　(5-6)　465-480　2007/07

DOI： 10.1007/s00153-007-0050-6 　

ISSN： 1432-0665
Complex analysis in subsystems of second order arithmetic Peer-reviewed

Keita Yokoyama

ARCHIVE FOR MATHEMATICAL LOGIC　46　(1)　15-35　2007/01

DOI： 10.1007/s00153-006-0017-z 　

ISSN： 1432-0665
Non-standard analysis in ACA(0) and Riemann mapping theorem Peer-reviewed

Keita Yokoyama

MATHEMATICAL LOGIC QUARTERLY　53　(2)　132-146　2007

DOI： 10.1002/malq.200610033 　

ISSN： 0942-5616

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Misc. 13

Very weak fragments of weak Kőnig's lemma

Stephen G. Simpson, Keita Yokoyama

2021/01/03

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It is well-known that any finite $\Pi^{0}_{1}$-class of $2^{\mathbb N}$ has a computable member. Then, how can we understand this in the context of reverse mathematics? In this note, we consider several very weak fragments of K\H{o}nig's lemma to answer this qeustion.
Recent studies on the proof-theoretic strength of Ramsey's theorem for pairs

Keita Yokoyama

in RIMS Kokyuroku　2016
A generalization of Levin-Schnorr's theorem

Keita Yokoyama

2013/10/11

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In this paper, we will generalize the definition of partially random or complex reals, and then show the duality of random and complex, i.e., a generalized version of Levin-Schnorr's theorem. We also study randomness from the view point of arithmetic using the relativization to a complete $\Pi^0_1$-class.
Notes on the first-order part of Ramsey's theorem for pairs

Keita Yokoyama

in RIMS Kokyuroku　1832　127-134　2013
Publisher: Kyoto University
ISSN： 1880-2818
Nonstandard arguments and recursive arguments

Keita Yokoyama

in RIMS Kokyuroku　1729　152-162　2011
Publisher: Kyoto University
ISSN： 1880-2818
Riceの定理のアナロジーについて (Japanese)

Hirohumi Yoshikawa, Keita Yokoyama

in RIMS Kokyuroku　1729　163-166　2011
Publisher: 京都大学
ISSN： 1880-2818
超準手法の逆数学と２階算術体系 (Japanese)

Keita Yokoyama

日本数学会, 数学基礎論および歴史分科会, 特別講演アブストラクト　36-50　2009
Standard and non-standard analysis in second order arithmetic

Keita Yokoyama

Tohoku Mathematical Publications　34　1-130　2009
Publisher: Tohoku University
ISSN： 1343-9499
Singularities of Holomorphic Functions in Subsystems of Second Order Arithmetic

Yoshihiro Horihata, Keita Yokoyama

in; Arnold Beckmann, Costas Dimitracopoulos, and Benedikt Löwe (eds.): Logic and Theory of Algorithms, Fourth Conference on Computability in Europe, CiE 2008, Athens, Greece, June 2008, Local Proceedings　157-164　2008
Reverse Mathematics for Fourier expansion

Keita Yokoyama

in; Arnold Beckmann, Costas Dimitracopoulos, and Benedikt Löwe (eds.): Logic and Theory of Algorithms, Fourth Conference on Computability in Europe, CiE 2008, Athens, Greece, June 2008, Local Proceedings　473-482　2008
２階算術における関数空間の扱いと超準解析的手法 (Japanese)

Keita Yokoyama

「算術体系の証明論」京都大学数理解析研究所講究録　1533　86-102　2007
Publisher: 京都大学
ISSN： 1880-2818
ACA0 のモデルの特徴付けと超準解析 (Japanese)

Keita Yokoyama

「自然数の超準モデルにおける１階定義可能性の研究」京都大学数理解析研究所講究録　1469　27-34　2006
Differential calculus in second order arithmetic

Keita Yokoyama

「証明論と計算論」京都大学数理解析研究所講究録　1442　122-148　2005
Publisher: Kyoto University
ISSN： 1880-2818

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Presentations 67

Reverse mathematics from multiple points of view Invited

Keita Yokoyama

International Congress of Mathematics 2022　2022/07/13
Reverse mathematics from multiple points of view Invited

Keita Yokoyama

Japan forum associated with ICM 2022　2022/06/13
Classifying theorems: reverse mathematics and its multiple viewpoints Invited

Keita Yokoyama

World Logic Day Workshop 2022　2022/01/17
Reverse mathematics and proof and model theory of arithmetic Invited

Keita Yokoyama

Computability in Europe 2021: Connecting with Computability
Forcing interpretation, conservation and proof size Invited

Keita Yokoyama

Proof Theory Virtual Seminar,　2021/02/17
Automorphism argument and reverse mathematics Invited

Keita Yokoyama

Computability Theory and Applications Online Seminar　2020/12/15
On the first-order consequences of Ramsey's theorem over RCA$_{0}^{*}$ Invited

Keita Yokoyama

Workshop on Proof Theory, Modal Logic and Reflection Principles　2019/11
Recent struggling for the first-order part of Ramsey's theorem for pairs International-presentation

Keita Yokoyama

Reverse Mathematics of Combinatorial Principles　2019/09
Recent progress on the study of the first-order part of Ramsey's theorem for pairs Invited

Keita Yokoyama

Mathematical Logic and Constructivity　2019/08
Approaching the first-order part of Ramsey's theorem for pairs and two colors Invited

Keita Yokoyama

Workshop on Computability Theory 2019
Finitary infinite pigeonhole principle and Ramsey's theorem in reverse mathematics

Keita Yokoyama

Computability in Europe 2019　2019/07
Terrence Tao's finitary infinite pigeonhole principle and proof-theory

Keita Yokoyama

2019 SJTU-JAIST-NU Follow-Up Workship on Formal Methods　2019/06
Weihrauch degrees of numerical problems Invited

Keita Yokoyama

Computability Theory and Foundations of Mathematics 2019
First-order parts of Weihrauch degrees

Keita Yokoyama

Third Workshop on Mathematical Logic and its Applications　2019/03
強い公理を要請する解析学の定理について

横山啓太

第6回山陰基礎論・解析学研究集会　2019/02
Ramsey's theorem and sizes of proofs Invited

Keita Yokoyama

Workshop on Ramsey Theory and Computability　2018/07
Ramsey's theorem in arithmetic Invited

Keita Yokoyama

2018 Winter Meeting of the Association of Symbolic Logic　2018/01
On the first-order part of Ramsey's theorem for pairs Invited

Keita Yokoyama

Computability Theory and Foundations of Mathematics 2017　2017/09
On the first-order strength of Ramsey's theorem in reverse mathematics Invited

Keita Yokoyama

Logic Colloquium 2017 (Special session on computability)　2017/08
Caristi's fixed point theorem in reverse mathematic Invited

Keita Yokoyama

Twelfth International Conference on Computability, Complexity and Randomness (CCR 2017)　2017/07
On the Proof-Theoretic Strength of Ramsey's Theorem for Pairs International-presentation Invited

Keita Yokoyama

Mathematical Logic and Its Applications　2016/09
Nonstandard methods in combinatorics International-presentation Invited

Keita Yokoyama

The 11th AIMS Conference on Dynamical Systems　2016/07
Thoughts on indicators and density notions International-presentation Invited

Keita Yokoyama

IMS-JSPS Joint Workshop on Mathematical Logic and the Foundations of Mathematics　2016/01
The proof-theoretic strength of Ramsey's theorem for pairs International-presentation Invited

Keita Yokoyama

New Challenges in Reverse Mathematics　2016/01
Paris's density notion and its infinite variations International-presentation Invited

Keita Yokoyama

JAF/MAMLS NYC　2015/07
Reverse mathematics and termination analysis International-presentation Invited

Keita Yokoyama

14th Asian Logic Conference　2015/01
Termination theorem and Ramsey's theorem International-presentation Invited

Keita Yokoyama

IMS-JSPS Joint Workshop in Mathematical Logic and Foundations of Mathematics　2014/09
Proof transformations for nonstandard analysis Invited

Keita Yokoyama

The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Special session 114: Nonstandard Analysis, Quantizations and Singular Perturbations　2014/07/10
Use of nonstandard models in reverse mathematics Invited

Keita Yokoyama

Journees sur les Arithmetiques Faibles 33　2014/06/17
The strength of Ramsey's theorem from several different view points

Keita Yokoyama

CORCON 2014 Workshop　2014/03/25
Finite iterations of infinite and finite Ramsey’s theorem

横山啓太

日本数学会　2014/03/15
Finite iterations of infinite and finite Ramsey’s theorem

Keita Yokoyama

Computability Theory and Foundations of Mathematics 2014　2014/02/18
Fast growing functions and Ramsey’s theorem

Keita Yokoyama

The 48th MLG meeting　2013/12/08
弱い組合わせ命題と超準的手法

横山啓太

超準解析シンポジウム　2013/09/18
On the second-order categoricity of the natural number system

横山啓太

証明論研究集会 2013　2013/08/08
On the strength of Ramsey's theorem without $\Sigma_1$-induction

Keita Yokoyama

Computability in Europe 2013　2013/07/04
A generalization of Levin/Schnorr's theorem

Keita Yokoyama

ELC Workshop on Randomness and Probability Through Computability　2013/05/14
Several versions of Friedman's self-embedding theorem

Keita Yokoyama

Computability Theory and Foundations of Mathematics　2013/02
Randomness and arithmetic

Keita Yokoyama

Fourth Workshop on Game-Theoretic Probability and Related Topics　2012/11/13
Reverse mathematics and second-order categoricity

Keita Yokoyama

The 47th MLG Meeting　2012/11
Some versions of Friedman's self-embedding theorem

Keita Yokoyama

日本数学会, 数学基礎論および歴史分科会　2012/09
Ramsey's theorem without $\Sigma_{1}$-induction

Keita Yokoyama

日本数学会, 数学基礎論および歴史分科会　2012/09
A generalization of Schnorr's theorem

Keita Yokoyama

日本数学会, 数学基礎論および歴史分科会　2012/09
Compressibility and arithmetic

Keita Yokoyama

RIMS研究集会「証明論と複雑性」　2012/09
A proof-theoretic approach for Nonstandard Analysis Invited

Keita Yokoyama

The 9th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Special session: Discrete/Continuous and Nonstandard Analysis　2012/07
On the reverse mathematics of Peano categoricity

Keita Yokoyama

Workshop on Proof Theory and Computability 2012 - Philosophical Frontiers in Reverse Mathematics　2012/02
On Ramsey's theorem for pairs

Keita Yokoyama

Workshop on Proof Theory and Computability Theory, Akiu Spa Hotel Iwanumaya　2011/02
Nonstandard priority argument

Keita Yokoyama

短期共同研究「形式体系と計算理論」　2010/10
A nonstandard counterpart of DNR

Keita Yokoyama, Kojiro Higuchi

Logic Colloquium 2010　2010/07
Comparing non-standard axioms with axioms of second-order arithmetic

Keita Yokoyama

Workshop on Constructive Aspects of Logic and Mathematics　2010/03
Reverse Mathematics for differential equations

Keita Yokoyama

Proof theory symposium 2009, ホテルリステル猪苗代　2010/02
超準手法の逆数学と２階算術体系 Invited

Keita Yokoyama

日本数学会, 数学基礎論および歴史分科会, 特別講演,　2009/09
Non-standard reverse mathematics and reverse non-standard mathematics

Keita Yokoyama

東北大学理学研究科数学専攻談話会　2009/04
Non-standard analysis in non-standard second order arithmetic

the Asian Logic Conference 2009　2009
Non-standard analysis in non-standard second order arithmetic

the Asian Logic Conference 2009　2009
Integration and differentiation in second order arithmetic

Workshop on Constructivism: Logic and Mathematics　2008
Reverse Mathematics for Fourier expansion

the fourth conference on Computability in Europe 2008　2008
Formalizing non-standard arguments in second order arithmetic

the Asian Logic Conference 2008　2008
超準２階算術体系について

短期共同研究「証明論と論理・計算の構造」　2008
WWKLと２階算術における解析学

日本数学会・数学基礎論および歴史分科会　2008
Non-standard analysis within second order arithmetic

Computability, Reverse Mathematics and Combinatorics　2008
Integration and differentiation in second order arithmetic

Workshop on Constructivism: Logic and Mathematics　2008
Reverse Mathematics for Fourier expansion

the fourth conference on Computability in Europe 2008　2008
Formalizing non-standard arguments in second order arithmetic

the Asian Logic Conference 2008　2008
超準２階算術体系について

短期共同研究「証明論と論理・計算の構造」　2008
WWKLと２階算術における解析学

日本数学会・数学基礎論および歴史分科会　2008
Non-standard analysis within second order arithmetic

Computability, Reverse Mathematics and Combinatorics　2008

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Research Projects 9

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
逆数学における分割順序数

横山啓太, SOLDA GIOVANNI

Offer Organization: 日本学術振興会

System: 科学研究費助成事業

Category: 特別研究員奨励費

Institution: 東北大学

2022/04/22 - 2024/03/31
Approaching proof theory from the viewpoint of proof size

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

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

2019/04/01 - 2023/03/31
Expanding reverse mathematics with multiple viewpoints

Yokoyama Keita

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Young Scientists (B)

Institution: Japan Advanced Institute of Science and Technology

2016/04/01 - 2020/03/31

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In this project, we investigated the complexity and difficulty of mathematical theorems from the view point of reverse mathematics. Especially, we developed some new techniques to analyze the strength of combinatorial principles such as Ramsey's theorem, and solved a long-standing open problem on the proof-theoretic strength of Ramsey's theorem for pairs. Besides the above, we introduced some arguments to apply the above result and related techniques to the termination analysis, the study of sizes of proofs, found a new phenomenon on the reverse mathematical study of functional analysis, and expanded the field of reverse mathematics with those new points of view.
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.
The start-up for reverse mathematics from various angles

YOKOYAMA Keita

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

2013/08/30 - 2015/03/31

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The purpose of this research is to develop several new approaches for the study of reverse mathematics, whose goal is to determine the strength of ordinary mathematical theorems from various angles. In this research, I investigated the proof-theoretic strength of several combinatorial principles and introduced several new methods to determine the proof-theoretic strength. I also found a new way to apply these results into the study of termination analysis.
Computational Aspects of Randomness and Their Structural Analysis via Nonstandard Methods

TANAKA Kazuyuki, YAMAZAKI Takeshi, SUZUKI Toshio, TADAKI Kohtaro, KURODA Satoru, YOKOYAMA Keita

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

2011/04/01 - 2015/03/31

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The main aim of this research is to cultivate systematic understanding of randomness via various logical methods such as non-standard analysis so that computational aspects of basic concepts about probability and games deeply correlated to randomness should be clarified. We focus on the following five topics. (1) Setting a logical framework of nonstandard arguments for constructive measure theory. (2) Investigating computational structures by randomness notions. (3) Determining the equilibrium points of game trees. (4) Elucidating physical meaning of Chaitin’s Omega. (5) Logical treatments for determinacy of games.
超準手法と算術の融合による逆数学プログラムと超準解析学の発展

横山啓太

Offer Organization: 日本学術振興会

System: 科学研究費助成事業

Category: 若手研究(B)

Institution: 東北大学

2009 - 2011

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前年度からの研究を拡張し,超準解析と算術の融合手法を算術における組み合わせ論等の諸種の問題に応用する可能性を探った.前年度までの研究で,公理化した超準解析の体系と2階算術の諸体系の強さの関係がある程度明確になったため,このアイデアを再起理論の手法と関連づけることやラムゼイの定理の強さを調べる研究等に適用することを目指して研究を行った. 再起理論との関連づけでは,樋口氏との共同研究により,前年度に行った2階算術の公理WWKLの超準的な特徴付けのアナロジーを考え,再起理論由来の算術公理DNRに超準的な特徴付けを与えた. また,再起理論におけるpriority argumentと超準的な手法を特定の条件下で組み合わせることを試み,Chong, Slaman, Yangらによるラムゼイの定理に関連したいくつかの保存性証明に別証明を与えた.また組に関するラムゼイの定理RT^2_2の強さを調べる研究に関連し,算術の超準モデルの手法によるBovykin, WeiermannのRT^2_2のП_2部分の特徴付けを一部拡張して,П_3,П_4部分の特徴付けを得た. 超準解析を用いた公理系と2階算術との比較としては,Sanders氏による,体系ERNAとП_1移行原理を用いた逆数学研究を,2階算術のものと比較・翻訳を目指す研究を行った.ERNA+П_1は,2階算術体系WKL 0と似たような逆数学的な振る舞いをする一方で,完全には一致しない部分もある.これまでに,ERNA+П_1は2階算術におけるパラメータを許さないΔO_2-CAと同じ強さを持つことが分かっており,より具体的な翻訳が得られるか等を今後の研究課題としている.
実解析学複素解析学及び幾何学の基礎についての逆数学的研究

横山啓太

Offer Organization: 日本学術振興会

System: 科学研究費助成事業

Category: 特別研究員奨励費

Institution: 東北大学

2006 - 2007

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数学基礎論の一分野である2階算術の諸体系についての研究,特に逆数学プログラムへの寄与を目的とした研究および,算術の体系のモデルについての研究を行った. 2階算術の諸体系についての研究では,昨年度までの研究で得られていたACA_0およびWKL_0における超準解析の手法についてより精密な考察を行った.これにより,2階算術に対応した超準解析の手法が直接表現できるシステムを新たに考案した.さらに,これらのシステムを用いて表現される超準解析の証明を通常の2階算術の証明に直接変換するための手続きを与えた.これにより,超準解析の証明を細かく分析することが可能になり,超準手法を用いた逆数学研究のための新たな手法が得られた.また,これらをさらに発展させ,2階算術の多くのシステムに対して超準解析のシステムによる特徴付けを行い,さらに超準解析を用いたより多くめ証明の分析を進めることを目指して研究を進めている.また,これらのフレームワークの逆数学研究への新たな応用も試みている. また,堀畑佳宏氏と協働で複素解析の基礎に関する逆数学研究をさらに推し進め,いくつかの定理に対する逆数学的な評価を得た.特に,局所的な可積分性が重要となる状況では,WWKL_0が重要な役割を果たすことがわかり,このことからいくつかの逆数学的な評価が得られた.また,正則関数の特異点の扱いについての研究も行った.現在,ピカールの定理の逆数学的評価を目指し,研究を進めている.この他,フーリエ級数の収束性についても逆数学研究を行い,いくつかの逆数学的結果を得た. 以上の結果をふまえ,今までの成果を博士論文「Standard and Non-standard Analysis in Second Order Arithmetic」にまとめた.

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Teaching Experience 4

Mathematical Logic　JAIST
Fundamental Mathematics for Information Science　JAIST
数理論理学　北陸先端科学技術大学院大学
基礎情報数学　北陸先端科学技術大学院大学

Social Activities 4

Second Workshop on Mathematical Logic and its Applications

Kanazawa Tokyu Hotel, Ishikawa, Japan

2018/03/05 - 2018/03/09
Computability Theory and Foundations of Mathematics 2016

Waseda University, Tokyo, Japan

2016/09/20 - 2016/09/21
Computability Theory and Foundations of Mathematics 2015

Tokyo Institute of Technology

2015/09/07 - 2015/09/11
Computability Theory and Foundations of Mathematics 2014

Tokyo Institute of Technology