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Construction of models of higher Chang conjectures and saturated ideals

Research Project

Project/Area Number 23540119
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionUniversity of Tsukuba

Principal Investigator

SHIOYA Masahiro  筑波大学, 数理物質系, 准教授 (30251028)

Co-Investigator(Renkei-kenkyūsha) ABE Yoshihiro  神奈川大学, 理学部, 教授 (10159452)
MATSUBARA Yo  名古屋大学, 情報文化学部, 教授 (30242788)
TSUBOI Akito  筑波大学, 数理物質系, 教授 (30180045)
Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords数理論理学 / 公理的集合論 / 無限組合せ論 / 巨大基数 / 強制法 / 反映原理 / 飽和イデアル / 稠密イデアル
Research Abstract

1. On the construction of a model in which higher Chang conjecture holds. Foreman constructed a model in which Chang conjecture holds for triples, but the case for quadruples remains open. As the first step toward the solution, we gave a much simpler construction of a model like Foreman's.
2. On the construction of a model that contains a saturated ideal. Woodin constructed a model that contains a dense ideal, but the corresponding Boolean algebra is not yet known. As the first step toward the solution, we constructed by two-step iterated forcing, a model that contains a strongly saturated ideal originally due to Laver, and that contains a centered ideal originally due to Laver and Foreman.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (12 results)

All 2013 2012 2011

All Journal Article (7 results) (of which Peer Reviewed: 4 results) Presentation (5 results)

  • [Journal Article] A model theoretic reflection principle revisited2013

    • Author(s)
      塩谷真弘
    • Journal Title

      RIMS Kokyuroku

      Volume: 1851 Pages: 72-86

    • URL

      http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/1851.html

    • Related Report
      2013 Final Research Report
  • [Journal Article] On skinny stationary subsets of Pκλ2013

    • Author(s)
      松原洋, 薄葉季路
    • Journal Title

      J. Symbolic Logic

      Volume: 78 Pages: 667-680

    • URL

      http://projecteuclid.org/euclid.jsl/1368627071

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] A model theoretic reflection principle revisited2013

    • Author(s)
      Masahiro Shioya
    • Journal Title

      RIMS Kokyuroku

      Volume: 1851

    • Related Report
      2013 Annual Research Report
  • [Journal Article] Notes on the partition property of Pκλ2012

    • Author(s)
      阿部吉弘, 薄葉季路
    • Journal Title

      Arch. Math. Logic

      Volume: 51 Pages: 575-589

    • URL

      http://link.springer.com/article/10.1007/s00153-012-0283-x

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the existence of indiscernible trees2012

    • Author(s)
      竹内耕太, 坪井明人
    • Journal Title

      Ann. Pure Appl. Logic

      Volume: 163 Pages: 1891-1902

    • NAID

      120007137191

    • URL

      http://www.sciencedirect.com/science/article/pii/S0168007212000978

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Locally o-minimal structures2012

    • Author(s)
      川上智宏, 田中浩, 竹内耕太, 坪井明人
    • Journal Title

      J. Math. Soc. Japan

      Volume: 64 Pages: 783-797

    • NAID

      10031177249

    • URL

      http://projecteuclid.org/euclid.jmsj/1343133743

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] The Easton collapse and a saturated filter2011

    • Author(s)
      塩谷真弘
    • Journal Title

      RIMS Kokyuroku

      Volume: 1754 Pages: 108-114

    • URL

      http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/1754.html

    • Related Report
      2013 Final Research Report
  • [Presentation] A simplified approach to saturated ideals2013

    • Author(s)
      塩谷真弘
    • Organizer
      Reflection Principles and Set Theory of Large Cardinals
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2013 Final Research Report
  • [Presentation] Simple proof of a basic result of forking2013

    • Author(s)
      坪井明人
    • Organizer
      Model Theoretic Aspects of the Notion of Independence and Dimension
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2013 Final Research Report
  • [Presentation] Real closed field as an extension of Q2013

    • Author(s)
      坪井明人
    • Organizer
      高知モデル理論研究集会
    • Place of Presentation
      高知工科大学
    • Related Report
      2013 Final Research Report
  • [Presentation] A simplified approach to saturated ideals2013

    • Author(s)
      Masahiro Shioya
    • Organizer
      Reflection principles and set theory of large cardinals
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2013 Annual Research Report
  • [Presentation] On small models2012

    • Author(s)
      坪井明人
    • Organizer
      モデル理論夏の勉強会
    • Place of Presentation
      東海大学山中湖セミナーハウス
    • Related Report
      2013 Final Research Report

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Published: 2011-08-05   Modified: 2019-07-29  

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