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Sakai Hiroshi  酒井 拓史

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酒井 拓史  サカイ ヒロシ

SAKAI Hiroshi  酒井 拓史

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Researcher Number 70468239
Affiliation (Current) 2020: 神戸大学, システム情報学研究科, 准教授
Affiliation (based on the past Project Information) *help 2020: 神戸大学, システム情報学研究科, 准教授
2018: 神戸大学, システム情報学研究科, 准教授
2016: 神戸大学, 大学院システム情報学研究科, 准教授
2015: 神戸大学, システム情報学研究科, 准教授
2013: 神戸大学, システム情報学研究科, 准教授 … More
2011 – 2012: 神戸大学, その他の研究科, 講師
2011: 神戸大学, システム情報学研究科, 講師
2011: 神戸大学, 大学院・システム情報学研究科, 講師 Less
Review Section/Research Field
Principal Investigator
General mathematics (including Probability theory/Statistical mathematics) / Basic Section 12030:Basic mathematics-related
Except Principal Investigator
General mathematics (including Probability theory/Statistical mathematics) / Foundations of mathematics/Applied mathematics / Basic Section 12030:Basic mathematics-related
Keywords
Principal Investigator
公理的集合論 / 反映原理 / 巨大基数公理 / 無限組み合わせ論 / 国際情報交換 / 国際研究者交流 / 多国籍 / 基数算術 / 巨大基数
Except Principal Investigator
数学基礎論 … More / 反映原理 / 公理的集合論 / 集合論的位相空間論 / 強制法 / 強制公理 / バナッハ・マズア型ゲーム / 巨大基数 / 基数不変量 / Fodor-type Reflection Principle / Rado's conjecture / chromatic number / list-chromatic number / coloring number / 位相空間 / 無限グラフ / ブール代数 / 距離付け可能性 / coloring Number / openly generatedなブール代数 / Coloring Number / Openly generatedなブール代数 / 無限ゲーム / 彩色数 / 強コンパクト基数 / ω1-強コンパクト基数 / レヴィ崩壊 / リスト彩色数 / 連続体問題 / 集合論的多世界宇宙 / 数学の基礎づけ Less
  • Research Projects

    (7 results)
  • Research Products

    (35 results)
  • Co-Researchers

    (13 People)
  •  Toward a solution of the Continuum Problem from the point of view of %% set-theoretic multiverseOngoing

    • Principal Investigator
      渕野 昌
    • Project Period (FY)
      2020 – 2023
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Review Section
      Basic Section 12030:Basic mathematics-related
    • Research Institution
      Kobe University
  •  Higher analogies of reflection principles and cardinal arithmeticPrincipal InvestigatorOngoing

    • Principal Investigator
      酒井 拓史
    • Project Period (FY)
      2018 – 2020
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Review Section
      Basic Section 12030:Basic mathematics-related
    • Research Institution
      Kobe University
  •  Research toward a solution of Galvin's conjecture

    • Principal Investigator
      Fuchino Sakae
    • Project Period (FY)
      2014 – 2015
    • Research Category
      Grant-in-Aid for Challenging Exploratory Research
    • Research Field
      Foundations of mathematics/Applied mathematics
    • Research Institution
      Kobe University
  •  Invariant structures on medium-size infinite cardinals

    • Principal Investigator
      YOSHINOBU YASUO
    • Project Period (FY)
      2012 – 2016
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      General mathematics (including Probability theory/Statistical mathematics)
    • Research Institution
      Nagoya University
  •  On reflection principles at small uncountable cardinalsPrincipal Investigator

    • Principal Investigator
      SAKAI Hiroshi
    • Project Period (FY)
      2011 – 2013
    • Research Category
      Grant-in-Aid for Young Scientists (B)
    • Research Field
      General mathematics (including Probability theory/Statistical mathematics)
    • Research Institution
      Kobe University
  •  Reflection principles on stationarity and possible extensions of the axiom system of set thoery

    • Principal Investigator
      FUCHINO Sakae
    • Project Period (FY)
      2009 – 2011
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      General mathematics (including Probability theory/Statistical mathematics)
    • Research Institution
      Kobe University
  •  Combinatorics on medium-sized infinite cardinals

    • Principal Investigator
      YASUO Yoshinobu (YOSHINOBU Yasuo)
    • Project Period (FY)
      2008 – 2011
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      General mathematics (including Probability theory/Statistical mathematics)
    • Research Institution
      Nagoya University

All 2019 2018 2015 2013 2012 2011 Other

All Journal Article Presentation

  • [Journal Article] On the existence of skinny stationary subsets2019

    • Author(s)
      Yo Matsubara, Hirosh Sakai, Toshimichi Usuba
    • Journal Title

      Annals of Pure and Applied Logic

      Volume: 170 Pages: 539-557

    • DOI

      10.1016/j.apal.2018.12.003

    • NAID

      120006604682

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-18K03397, KAKENHI-PROJECT-18K03403, KAKENHI-PROJECT-18K03404
  • [Journal Article] Stationary reflection principles and two cardinal tree properties2015

    • Author(s)
      Hiroshi Sakai and Boban Velickovic
    • Journal Title

      Journal of the Institute of Mathematics of Jussieu

      Volume: 掲載確定 Pages: 69-85

    • DOI

      10.1017/s1474748013000315

    • NAID

      120005848133

    • Peer Reviewed / Open Access
    • Data Source
      KAKENHI-PROJECT-23740076, KAKENHI-PROJECT-26610040
  • [Journal Article] Simple proofs of SCH from reflection principles without using better scales2015

    • Author(s)
      Hiroshi Sakai
    • Journal Title

      Archive for Mathematical Logic

      Volume: 54 Pages: 639-647

    • DOI

      10.1007/s00153-015-0432-0

    • NAID

      120005848132

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-26610040
  • [Journal Article] Reflection and indescribability in the constructible universe2015

    • Author(s)
      Joan Bagaria, Menachem Magidor, and Hiroshi Sakai
    • Journal Title

      Israel Journal of Mathematics

      Volume: 208 Pages: 1-11

    • Peer Reviewed / Acknowledgement Compliant / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-26610040
  • [Journal Article] Reflection and indescribability in the constructible universe2015

    • Author(s)
      Joan Bagaria, Hiroshi Sakai and Menachem Magidor
    • Journal Title

      Israel Journal of Mathematics

      Volume: 未定

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-26610040
  • [Journal Article] Chang's conjecture and weak square2013

    • Author(s)
      Hiroshi Sakai
    • Journal Title

      Archive for Mathematical Logic

      Volume: 52

    • DOI

      10.1007/s00153-012-0305-8

    • NAID

      120005367491

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-23740076
  • [Journal Article] Chang's conjecture and weak square2013

    • Author(s)
      H. Sakai
    • Journal Title

      Archive for Mathematical Logic

      Volume: Vol.52, No.1-2 Pages: 29-45

    • NAID

      120005367491

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-23740076
  • [Journal Article] On proofs of the incompleteness theorems based on Berry's paradox by Vopenka, Chaitin, and Boolos2012

    • Author(s)
      Makoto Kikuchi, Taishi Kurahashi, Hiroshi Sakai
    • Journal Title

      Mathematical Logic Quarterly

      Volume: 57 Pages: 307-316

    • DOI

      10.1002/malq.201110067

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-23740076, KAKENHI-PROJECT-24540125
  • [Journal Article] On proofs of the incompleteness theorems based on Berry's paradox by Vopenka, Chaitin, and Boolos2012

    • Author(s)
      M. Kikuchi, T. Kurahashi and H. Sakai
    • Journal Title

      Mathematical Logic Quarterly

      Volume: Vol.58 ,No.4-5 Pages: 307-316

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-23740076
  • [Journal Article] On proofs of the incompleteness theorem based on Berry's paradox by Vopenka, Boolos and Chaitin2012

    • Author(s)
      酒井拓史,倉橋太志,菊池誠
    • Journal Title

      Mathematical Logic Quarterly

      Volume: 58

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-23740076
  • [Journal Article] Partial square at \omega_1 is impied by MM but not by PFA2011

    • Author(s)
      酒井拓史
    • Journal Title

      Fundamenta Mathematicae

      Volume: 215 Pages: 109-131

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-23740076
  • [Journal Article] Partial square at omega_1 is implied by MM but not by PFA2011

    • Author(s)
      H. Sakai
    • Journal Title

      Fundamenta Mathematicae

      Volume: Vol.215,No.2 Pages: 109-131

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-23740076
  • [Journal Article] On standard model ofMartin's Maximum2011

    • Author(s)
      H. Sakai
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: No.1754 Pages: 97-107

    • Data Source
      KAKENHI-PROJECT-23740076
  • [Journal Article] Reflection and indescribability in the constructible universe

    • Author(s)
      J. Bagaria, M. Magidor and H. Sakai
    • Journal Title

      Israel Journal of Mathematics

      Volume: (掲載決定)

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-23740076
  • [Journal Article] Stationary reflection principles and two cardinal tree properties

    • Author(s)
      H. Sakai and B. Velickovic
    • Journal Title

      Journal of the Institute of Mathematics of Jussieu

      Volume: (掲載決定)

    • NAID

      120005848133

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-23740076
  • [Presentation] On generalized notion of higher stationarity in P_kappa ( lambda )2018

    • Author(s)
      Hiroshi Sakai
    • Organizer
      RIMS Workshop "Axiomatic Set Theory and its Applications"
    • Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-18K03397
  • [Presentation] On generalized notion of higher stationarity in P_kappa ( lambda )2018

    • Author(s)
      Hiroshi Sakai
    • Organizer
      Reflections on Set Theoretic Reflection
    • Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-18K03397
  • [Presentation] Proof of SCH from reflection principles without using scales2015

    • Author(s)
      Hiroshi Sakai
    • Organizer
      Sets and Computations
    • Place of Presentation
      National University of Singapore
    • Year and Date
      2015-04-02
    • Invited
    • Data Source
      KAKENHI-PROJECT-26610040
  • [Presentation] Separation of MA^+ (sigma-closed) from reflection principles2013

    • Author(s)
      H. Sakai
    • Organizer
      ESI Workshop Forcing and Large Cardinals
    • Place of Presentation
      Erwin Schrodinger Institute,ウィーン(オーストリア)
    • Year and Date
      2013-09-24
    • Data Source
      KAKENHI-PROJECT-23740076
  • [Presentation] n-stationary and Pi^1_n-1-indescribable sets2013

    • Author(s)
      H. Sakai
    • Organizer
      RIMS共同利用研究集会反映原理と巨大基数の集合論
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2013-09-11
    • Data Source
      KAKENHI-PROJECT-23740076
  • [Presentation] 定常性反映原理と半定常性反映原理(特別講演)2013

    • Author(s)
      酒井拓史
    • Organizer
      日本数学会年会
    • Place of Presentation
      京都大学
    • Year and Date
      2013-03-21
    • Data Source
      KAKENHI-PROJECT-23740076
  • [Presentation] Separation of MA^+ (sigma-closed) from reflection principles2013

    • Author(s)
      H. Sakai
    • Organizer
      International Conference on Topology and Geometry2013
    • Place of Presentation
      島根大学
    • Year and Date
      2013-09-05
    • Invited
    • Data Source
      KAKENHI-PROJECT-23740076
  • [Presentation] Consequences of Martin's Maximum and weak square2012

    • Author(s)
      H. Sakai
    • Organizer
      Workshop of Forcing Axioms and their Applications
    • Place of Presentation
      Fields Institute,トロント(カナダ)
    • Year and Date
      2012-10-24
    • Invited
    • Data Source
      KAKENHI-PROJECT-23740076
  • [Presentation] Fragments of Martin's Maximum and weak square2012

    • Author(s)
      酒井拓史
    • Organizer
      ASL 2012 North American Annual Meeting(招待講演)
    • Place of Presentation
      University of Wisconsin-Madison (United States of America)
    • Data Source
      KAKENHI-PROJECT-23740076
  • [Presentation] Fragments of Martin's Maximum and weak square2012

    • Author(s)
      H. Sakai
    • Organizer
      Association for Symbolic Logic 2012 North American Annual Meeting
    • Place of Presentation
      University of Wisconsin-Madison,マディソン(アメリカ)
    • Year and Date
      2012-03-31
    • Invited
    • Data Source
      KAKENHI-PROJECT-23740076
  • [Presentation] Chang's Conjecture and weak square2011

    • Author(s)
      酒井拓史
    • Organizer
      京都大学数理解析研究所 共同利用研究集会「記述集合論の展望」
    • Place of Presentation
      京都大学数理解析研究所(京都府)
    • Data Source
      KAKENHI-PROJECT-23740076
  • [Presentation] Chang's conjecture and weak square2011

    • Author(s)
      H. Sakai
    • Organizer
      RIMS共同利用研究集会記述集合論の展望
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2011-10-20
    • Data Source
      KAKENHI-PROJECT-23740076
  • [Presentation] Chang's conjecture and weak square2011

    • Author(s)
      H. Sakai
    • Organizer
      the 12th Asian Logic Conference
    • Place of Presentation
      Victoria University of Wellington,ウェリントン(ニュージーランド)
    • Year and Date
      2011-12-17
    • Data Source
      KAKENHI-PROJECT-23740076
  • [Presentation] Chang's Conjecture and weak square2011

    • Author(s)
      酒井拓史
    • Organizer
      12th Asian Logic Conference
    • Place of Presentation
      Victoria University of Wellington (New Zealand)
    • Data Source
      KAKENHI-PROJECT-23740076
  • [Presentation] Fragments of Martin's Maximum and weak square

    • Author(s)
      Hiroshi Sakai
    • Organizer
      ASL 2012 North American Annual Meeting
    • Place of Presentation
      University of Wisconsin-Madison
    • Invited
    • Data Source
      KAKENHI-PROJECT-23740076
  • [Presentation] 定常性反映原理と半定常性反映原理

    • Author(s)
      酒井 拓史
    • Organizer
      日本数学会年会
    • Place of Presentation
      京都大学
    • Invited
    • Data Source
      KAKENHI-PROJECT-23740076
  • [Presentation] Consequences of Martin's Maximum and weak square

    • Author(s)
      Hiroshi Sakai
    • Organizer
      Workshop on Forcing Axioms and their Applications
    • Place of Presentation
      Fields Institute
    • Invited
    • Data Source
      KAKENHI-PROJECT-23740076
  • [Presentation] Separation of MA^+ (sigma-closed) from reflection principles

    • Author(s)
      Hiroshi Sakai
    • Organizer
      International Conference on Topology and Geometry 2013
    • Place of Presentation
      島根大学
    • Invited
    • Data Source
      KAKENHI-PROJECT-23740076
  • [Presentation] n-stationary and Pi^1_n-1-stationary sets

    • Author(s)
      Hiroshi Sakai
    • Organizer
      RIMS Workshop "Reflection principles and set theory of large cardinals"
    • Place of Presentation
      京都大学数理解析研究所
    • Data Source
      KAKENHI-PROJECT-23740076
  • [Presentation] Separation of MA^+ (sigma-closed) from reflection principles

    • Author(s)
      Hiroshi Sakai
    • Organizer
      Erwin Schrodinger Institute Workshop "Forcing and Large Cardinals"
    • Place of Presentation
      Erwin Schrodinger Institute, ウィーン(オーストリア)
    • Invited
    • Data Source
      KAKENHI-PROJECT-23740076
  • 1.  FUCHINO Sakae (30292098)
    # of Collaborated Projects: 5 results
    # of Collaborated Products: 0 results
  • 2.  USUBA Toshimichi (10513632)
    # of Collaborated Projects: 4 results
    # of Collaborated Products: 1 results
  • 3.  YASUO Yoshinobu (90281063)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 4.  MATSUBARA Yo (30242788)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 5.  MIYAMOTO Tadatoshi (70229889)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 6.  KADA Masaru (00312447)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 7.  TOMOYASU Kazuo (10332107)
    # of Collaborated Projects: 2 results
    # of Collaborated Products: 0 results
  • 8.  LAJOS Soukup
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 9.  FRIEDMAN Sy-david
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 10.  KONIG Bernhard
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 11.  B.LARSON Paul
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 12.  König Bernhard
    # of Collaborated Projects: 1 results
    # of Collaborated Products: 0 results
  • 13.  菊池 誠
    # of Collaborated Projects: 0 results
    # of Collaborated Products: 1 results

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