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Combinatorics on medium-sized infinite cardinals

Research Project

Project/Area Number 20540114
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionNagoya University

Principal Investigator

YASUO Yoshinobu (YOSHINOBU Yasuo)  名古屋大学, 情報科学研究科, 准教授 (90281063)

Co-Investigator(Renkei-kenkyūsha) FUCHINO Sakae  神戸大学, 大学院・システム情報学研究科, 教授 (30292098)
MATSUBARA Yo  名古屋大学, 大学院・情報科学研究科, 教授 (30242788)
MIYAMOTO Tadatoshi  南山大学, 経営学部, 教授 (70229889)
KADA Masaru  大阪府立大学, 大学院・理学系研究科, 准教授 (00312447)
TOMOYASU Kazuo  都城工業高等専門学校, 一般科目理科, 准教授 (10332107)
Research Collaborator SAKAI Hiroshi  神戸大学, 大学院・システム情報学研究科, 講師 (70468239)
USUBA Toshimichi  名古屋大学, 高等研究院, 特任助教 (10513632)
KONIG Bernhard  (元)トロント大学, 客員研究員
B.LARSON Paul  マイアミ大学, 教授
Project Period (FY) 2008 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords数学基礎論 / 公理的集合論 / 集合論的位相空間論 / 強制法 / 強制公理 / 反映原理 / 基数不変量 / バナッハ・マズア型ゲーム
Research Abstract

Combinatorics of infinite cardinals greater than or equal to aleph 2 take on a different aspect from that of aleph 1, that is, the least uncountable cardinal. In this research, we studied inherent combinatorial nature of relatively small infinite cardinals greater than or equal to aleph 2, from the aspect of its interaction with several well-known axioms of set theory and that of its influence on set-theoretic topology, and obtained several significant results in this area.

Report

(6 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report   Self-evaluation Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (25 results)

All 2013 2012 2011 2010 2009 2008 Other

All Journal Article (6 results) (of which Peer Reviewed: 6 results) Presentation (19 results)

  • [Journal Article] Operations,climbability and the proper forcing axiom2013

    • Author(s)
      Yasuo Yoshinobu
    • Journal Title

      Annals of Pure and Applied Logic

      Volume: vol.164,no.7-8 Issue: 7-8 Pages: 749-762

    • DOI

      10.1016/j.apal.2012.11.010

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Kurepa trees and Namba forcing2012

    • Author(s)
      Bernhard Koenig and Yasuo Yoshinobu
    • Journal Title

      Journal of Symbolic Logic

      Volume: vol.77,no.4 Issue: 4 Pages: 1281-1290

    • DOI

      10.2178/jsl.7704130

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Galois-Tukey connection involving sets of metrics2012

    • Author(s)
      Masaru Kada and Yasuo Yoshinobu
    • Journal Title

      Tsukuba Journal of Mathematics

      Volume: vol.36,no.1 Pages: 53-66

    • NAID

      120006349361

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Dense non-reflection for stationary collections of countable sets2009

    • Author(s)
      David Aspero, John Krueger and Yasuo Yoshinobu
    • Journal Title

      Annals of Pure and Applied Logic

      Volume: vol.161,no.1 Issue: 1 Pages: 94-108

    • DOI

      10.1016/j.apal.2009.06.002

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Dense non-reflection for stationary collection of countable sets2009

    • Author(s)
      David Aspero, John Krueger, Yasuo Yoshinobu
    • Journal Title

      Annals of Pure and Applied Logic 161(1)

      Pages: 94-108

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Dense non-reflection for stationary collections of countable sets2009

    • Author(s)
      David Aspero, John Krueger, Yasuo Yoshinobu
    • Journal Title

      Annals of Pure and Applied Logic 161(1)

      Pages: 94-108

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] 距離関数の順序構造とGalois-Tukey connection2012

    • Author(s)
      嘉田勝,吉信康夫
    • Organizer
      2012年度日本数学会秋季総合分科会トポロジー分科会
    • Place of Presentation
      九州大学
    • Year and Date
      2012-09-18
    • Related Report
      2011 Final Research Report
  • [Presentation] On weakly operationally closed posets2012

    • Author(s)
      Yasuo Yoshinobu
    • Organizer
      FMF/JSPS joint seminar on Forcing in Set Theory
    • Place of Presentation
      神戸大学
    • Year and Date
      2012-01-23
    • Related Report
      2011 Final Research Report
  • [Presentation] The Banach-Mazur game with imperfect recall2011

    • Author(s)
      Yasuo Yoshinobu
    • Organizer
      京都大学数理解析研究所研究集会「記述集合論の展望」
    • Place of Presentation
      京都大学
    • Year and Date
      2011-10-19
    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [Presentation] 強制法と位相空間の被覆の性質について2011

    • Author(s)
      薄葉季路,吉信康夫
    • Organizer
      2011年度日本数学会秋季総合分科会トポロジー分科会
    • Place of Presentation
      信州大学
    • Year and Date
      2011-09-30
    • Related Report
      2011 Final Research Report
  • [Presentation] 強制法と位相空間の被覆の性質について2011

    • Author(s)
      薄葉季路・吉信康夫
    • Organizer
      2011年度日本数学会秋季総合分科会(トポロジー分科会一般講演)
    • Place of Presentation
      信州大学
    • Year and Date
      2011-09-30
    • Related Report
      2010 Annual Research Report
  • [Presentation] Lindelof空間とHechler強制2011

    • Author(s)
      足立裕基,薄葉季路,吉信康夫
    • Organizer
      2011年度日本数学会秋季総合分科会数学基礎論及び歴史分科会
    • Place of Presentation
      信州大学
    • Year and Date
      2011-09-28
    • Related Report
      2011 Final Research Report
  • [Presentation] Lindelof空間とHechler強制2011

    • Author(s)
      足立裕基・薄葉季路・吉信康夫
    • Organizer
      2011年度日本数学会秋季総合分科会(数学基礎論及び歴史分科会一般講演)
    • Place of Presentation
      信州大学
    • Year and Date
      2011-09-28
    • Related Report
      2010 Annual Research Report
  • [Presentation] Climbability properties and the strong non-reflection2011

    • Author(s)
      吉信康夫
    • Organizer
      神奈川大学集合論セミナー
    • Place of Presentation
      神奈川大学
    • Year and Date
      2011-09-03
    • Related Report
      2011 Final Research Report 2010 Annual Research Report
  • [Presentation] 強制法のもとでの被覆の性質の保存について2011

    • Author(s)
      薄葉季路,吉信康夫
    • Organizer
      第46回位相空間論シンポジウム
    • Place of Presentation
      静岡大学
    • Year and Date
      2011-06-03
    • Related Report
      2011 Final Research Report 2010 Annual Research Report
  • [Presentation] Set theoretic aspects of Lindelof spaces2010

    • Author(s)
      足立裕基,薄葉季路,吉信康夫
    • Organizer
      2010年度General Topologyシンポジウム
    • Place of Presentation
      筑波大学
    • Year and Date
      2010-12-21
    • Related Report
      2011 Final Research Report 2010 Annual Research Report 2010 Self-evaluation Report
  • [Presentation] How many miles to βX, after all?2010

    • Author(s)
      嘉田勝,友安一夫,吉信康夫
    • Organizer
      2010年度General Topologyシンポジウム
    • Place of Presentation
      筑波大学
    • Year and Date
      2010-12-20
    • Related Report
      2011 Final Research Report 2010 Annual Research Report 2010 Self-evaluation Report
  • [Presentation] 半順序集合上のゲームとPFA2009

    • Author(s)
      吉信康夫
    • Organizer
      2009年度日本数学会秋季総合分科会数学基礎論及び歴史分科会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-26
    • Related Report
      2011 Final Research Report
  • [Presentation] 半順序集合上のゲームとPFA2009

    • Author(s)
      吉信康夫
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-26
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] 半順序集合上のゲームとPFA2009

    • Author(s)
      吉信康夫
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      大阪大学豊中キャンパス
    • Year and Date
      2009-09-26
    • Related Report
      2009 Annual Research Report
  • [Presentation] Forcing axioms and closure properties of posets2008

    • Author(s)
      Yasuo Yoshinobu
    • Organizer
      The 10th Asian Logic Conference
    • Place of Presentation
      神戸大学
    • Year and Date
      2008-09-03
    • Related Report
      2011 Final Research Report
  • [Presentation] Forcing axioms and closure properties of posets2008

    • Author(s)
      Yasuo Yoshinobu
    • Organizer
      The 10^<th> Asian Logic Conference
    • Place of Presentation
      神戸大学
    • Year and Date
      2008-09-03
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] Forcing axioms and closure properties of posets2008

    • Author(s)
      Yasuo Yoshinobu
    • Organizer
      The 10th Asian Logic Conference
    • Place of Presentation
      神戸大学(兵庫県神戸市)
    • Year and Date
      2008-09-03
    • Related Report
      2008 Annual Research Report
  • [Presentation] On weakly opreationally closed posets

    • Author(s)
      Yasuo Yoshinobu
    • Organizer
      FMF/JSPS joint seminar on Forcing in Set Theory
    • Place of Presentation
      神戸大学
    • Related Report
      2011 Annual Research Report
  • [Presentation] 距離関数の順序構造とGalois-Tukey connection

    • Author(s)
      嘉田勝, 吉信康夫
    • Organizer
      日本数学会秋季総合分科会トポロジー分科会
    • Place of Presentation
      九州大学
    • Related Report
      2011 Annual Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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