Set Theory of the Reals and its Applications

• Project/Area Number: 19540127
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kobe University
• Principal Investigator: BRENDLE Jorg Kobe University, 大学院・工学研究科, 准教授 (70301851)
• Project Period (FY): 2007 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥5,330,000 (Direct Cost: ¥4,100,000、Indirect Cost: ¥1,230,000); Fiscal Year 2008: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000); Fiscal Year 2007: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
• Keywords: 数学基礎論 / 集合論 / トポロジー / 測度論 / 強制法 / 組合せ論的集合論 / 記述集合論 / 数理論理学 / 連続体の基数不変量

Research Abstract

独立性証明というのは、数学的な命題が数学の標準的な公理系のもとでは証明できないことを示すための論法のことである。独立性証明を行う際の主要な集合論的な技法である強制法を用いることによって、実数の集合論、組合せ論的集合論、記述集合論や、一般位相幾何学などの様々な数学の分野における問題に関するいくつかの無矛盾性の結果を証明した。

Research Products

• [Journal Article] Stevo Todorcevic, Rectangular axioms, perfect set properties, and decomposition, Bulletin, Classe des Sciences Mathematiques et Naturelles, Sciences mathematiques (2008)
  • Author(s): Jorg Brendle, Paul Larson
  • Journal Title: Academie Serbe des Sciences et Arts, Beograd 33 Pages: 91-130
  • Peer Reviewed
• [Journal Article] Rectangular axioms, perfect set properties, and decomposition (2008)
  • Author(s): Jorg Brendle
  • Journal Title: Bulletin, Classe des Sciences Mathematiques et Naturelles, Sciences mathematiques, Academie Serbe des Sciences et Arts, Beograd 33 Pages: 91-130
  • Peer Reviewed
• [Journal Article] Mad families and ultrafilters, Acta Universitatis Carolinae (2007)
  • Author(s): Jorg Brendle
  • Journal Title: Mathematica et Physica 49 Pages: 19-35
  • Peer Reviewed
• [Journal Article] Coloring ordinals by reals (2007)
  • Author(s): Jorg Brendle, Sakae Fuchino
  • Journal Title: Fundamenta Mathematicae 196 Pages: 151-195
  • Peer Reviewed
• [Journal Article] Distinguishing groupwise density numbers (2007)
  • Author(s): Jorg Brendle
  • Journal Title: Monatshefte fur Mathematik 152 Pages: 207-215
  • Peer Reviewed
• [Journal Article] MAD families with strong combinatorial properties (2007)
  • Author(s): Jorg Brendle and Greg Piper
  • Journal Title: Fundamenta Mathematicae 193 Pages: 7-21
  • Peer Reviewed
• [Journal Article] Independence for distributivity numbers, in : Algebra, Logic, Set Theory. Festschrift fur Ulrich Felgner zum 65 (2007)
  • Author(s): Jorg Brendle
  • Journal Title: Geburtstag (B. Lowe, ed.), Studies in Logic (College Publications) vol. 4 Pages: 63-84
  • Peer Reviewed
• [Journal Article] Coloring ordinals by reals (2007)
  • Author(s): Jorg Brendle
  • Journal Title: Fundamenta Mathematicae 196 Pages: 151-195
  • Peer Reviewed
• [Journal Article] Mad families and ultrafilters (2007)
  • Author(s): Jorg Brendle
  • Journal Title: Acta Universitatis Carolinae. Mathematica et Physica 49 Pages: 19-35
  • Peer Reviewed
• [Journal Article] Countable Frechet Boolean groups : an independence result
  • Author(s): Jorg Brendle, Michael Hrusak
  • Journal Title: The Journal of Symbolic Logic, to appear
  • Peer Reviewed
• [Journal Article] Countable Brechet Boolean groups : an independence result
  • Author(s): Jorg Brendle
  • Journal Title: The Journal of Symbolic Logic 掲載決定(掲載決定)
  • Peer Reviewed
• [Presentation] Mad families on uncountable cardinals (2009)
  • Author(s): Jorg Brendle
  • Organizer: Jornadascolombo-venezolanas de teoria deconjuntos
  • Place of Presentation: Bogota, コロンビア
  • Year and Date: 2009-02-06
• [Presentation] Mad families on uncountable cardinals (2009)
  • Author(s): Jorg Brendle
  • Organizer: Jornadas Colombo-venezolanas de teoria de conjuntos
  • Place of Presentation: ボゴタ, コロンビア
  • Year and Date: 2009-02-06
• [Presentation] Recent results on madfamilies, Advances in Set-theoretic Topology (2008)
  • Author(s): Jorg Brendle
  • Organizer: Conference in Honour of Tsugunori Nogura on his 60th Birthday
  • Place of Presentation: Erice, イタリア
  • Year and Date: 2008-06-10
• [Presentation] Recent results on mad families (2008)
  • Author(s): Jorg Brendle
  • Organizer: Advances in Set-theoretic Topology, Conference in Honour of Tsugunon Nogura on his 60th Birthday
  • Place of Presentation: エリチエ, イタリア
  • Year and Date: 2008-06-10
• [Presentation] Mad families on singular cardinals (2008)
  • Author(s): Jorg Brendle
  • Organizer: Set Theory Meeting in Kobe
  • Place of Presentation: 神戸, 日本
  • Year and Date: 2008-03-21
• [Presentation] MAD families on singular cardinals (2008)
  • Author(s): Jorg Brendle
  • Organizer: Mengenlehre-Tagung
  • Place of Presentation: Oberwolfach, ドイツ
  • Year and Date: 2008-01-14
• [Presentation] MAD families on singular cardinals (2008)
  • Author(s): Jorg Brendle
  • Organizer: Mengenlehre-Tagung
  • Place of Presentation: Oberwolfach(ドイツ)
  • Year and Date: 2008-01-14
• [Presentation] Malyhin's Problem (2007)
  • Author(s): Jorg Brendle
  • Organizer: International Conference on Topology and its Applications
  • Place of Presentation: 京都, 日本
  • Year and Date: 2007-12-04
• [Presentation] Malyhin's Problem (2007)
  • Author(s): Jorg Brendle
  • Organizer: International Conference on Topology and its Applications
  • Place of Presentation: 京都(日本)
  • Year and Date: 2007-12-04
• [Presentation] Distinguishing groupwise density numbers (2007)
  • Author(s): Jorg Brendle
  • Organizer: Conference in honour of the 60th birthday of Professor Andreas R. Blass
  • Place of Presentation: Toronto, カナダ
  • Year and Date: 2007-11-10
• [Presentation] Distinguishing groupwise density numbers (2007)
  • Author(s): Jorg Brendle
  • Organizer: Conference in honour of the 60th birthday of Professor Andreas R. Blass
  • Place of Presentation: トロント(カナダ)
  • Year and Date: 2007-11-10
• [Presentation] What are cardinal invariants of the continuum (2007)
  • Author(s): Jorg Brendle
  • Organizer: Euler and modern combinatorics
  • Place of Presentation: St. Petersburg, ロシア
  • Year and Date: 2007-06-06
• [Presentation] What are cardinal invariants of the continuum? (2007)
  • Author(s): Jorg Brendle
  • Organizer: Euler and modern combinatorics
  • Place of Presentation: サンクト・ペテルブルグ(ロシア)
  • Year and Date: 2007-06-06
• [Remarks] 研究集会「Set Theory Meeting in Kobe」(神戸大学、2008年3月19日~21日)
  • URL: http://kurt.scitec.kobe-u.ac.jp/~brendle/other-meetings/kobe-march2008.html
• [Remarks] 研究集会「組合せ論的集合論と記述集合論」(京都大学、2008年8月25日~29日)
  • URL: http://kurt.scitec.kobe-u.ac.jp/~brendle/rims2008/j-home.html
• [Remarks] 国際会議「10th Asian Logic Conference」(神戸大学、2008年9月1日~6日)
  • URL: http://kurt.scitec.kobe-u.ac.jp/ALC10/
• [Remarks] 研究集会「第8回の関西集合論セミナー」(神戸大学、2009年3月5日~6日)
  • URL: http://kurt.scitec.kobe-u.ac.jp/~brendle/other-meetings/kobe-march2009.html