Combinatorics on aleph 1 and forcing theory

2009 Fiscal Year Final Research Report

• Project/Area Number: 19740048
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Shizuoka University
• Principal Investigator: YORIOKA Teruyuki Shizuoka University, 理学部, 准教授 (60432192)
• Project Period (FY): 2007 – 2009
• Keywords: 公理的集合論

Research Abstract

In this research, I studied about combinatorics on aleph 1. In particular, I investigated combinatorics about Aronszajn trees and introduced forcing axioms related to its combinatorics. In this research, I gave a new development about famous open problems on fragments of Martin's Axiom which has been introduced and deeply studied by Stevo Todorcevic.

Research Products

• [Journal Article] Uniformizing ladder system colorings and the rectangle refining property (2010)
  • Author(s): Teruyuki Yorioka
  • Journal Title: Proceedings of the American Mathematical Society 138 Pages: 2961-2971
  • Peer Reviewed
• [Journal Article] A non-implication between fragments of Martin's Axiom related to a property which comes from Aronszajn trees (2010)
  • Author(s): Teruyuki Yorioka
  • Journal Title: Annals of Pure and Applied Logic 161, no.4 Pages: 469-487
  • Peer Reviewed
• [Journal Article] Rudin's Dowker space in the extension with a Suslin tree (2008)
  • Author(s): Teruyuki Yorioka
  • Journal Title: Fundamenta Mathematicae 201 Pages: 53-89
  • Peer Reviewed
• [Journal Article] The inequality b>N_1 can be considered as an analogue of Suslin's Hypothesis, Axiomatic Set Theory and Set-theoretic Topology (Kyoto 2007) (2008)
  • Author(s): Teruyuki Yorioka
  • Journal Title: Surikaisekikenkyusho Kokyuroku No.1595 Pages: 84-88
• [Journal Article] Some weak fragments of Martin's Axiom related to the rectangle refining property (2008)
  • Author(s): Teruyuki Yorioka
  • Journal Title: Archive for Mathematical Logic 47 Pages: 79-90
  • Peer Reviewed
• [Presentation] ランダム実数を付け加えないCCC強制法の新しい例とPrikryとShelahの問題について (2009)
  • Author(s): 依岡輝幸
  • Organizer: 2009年度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
• [Presentation] CCC without random reals (2009)
  • Author(s): Teruyuki Yorioka
  • Organizer: ESI workshop on large cardinals and descriptive set theory, Erwin Schrodinger Instite
  • Place of Presentation: Vienna, Austria.
  • Year and Date: 2009-06-18
• [Presentation] カルキン環の射影作用素からなる極大鎖の長さについて (2009)
  • Author(s): 依岡輝幸
  • Organizer: 2009年度日本数学会年会
  • Place of Presentation: 東京大学
  • Year and Date: 2009-03-28
• [Presentation] Two properties which come from Aronszajn trees (2008)
  • Author(s): Teruyuki Yorioka
  • Organizer: The 10th Asian Logic Conference
  • Place of Presentation: 神戸大学
  • Year and Date: 2008-09-06
• [Presentation] A generalization of Rudin's Dowker space with a Suslin tree (2008)
  • Author(s): Teruyuki Yorioka
  • Organizer: Advances in Set-Theoretic Topology (in Honour of Tsugunori Nogura on his 60th Birthday), Centre for Scientific Culture "Ettore Majorana"
  • Place of Presentation: Erice, Sicily, Italy.
  • Year and Date: 2008-06-12
• [Presentation] A generalization of Rudin's Dowker space with a Suslin tree (2007)
  • Author(s): Teruyuki Yorioka
  • Organizer: International Conference on Topology and its Applications 2007
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2007-12-05
• [Presentation] Fragments of Martin's Axiom Related to the Rectangle Refining Property (2007)
  • Author(s): Teruyuki Yorioka
  • Organizer: Logic Colloquium 2007
  • Place of Presentation: Wroclaw, Poland.
  • Year and Date: 2007-07-15
• [Remarks] ホームページ
  • URL: http://www.ipc.shizuoka.ac.jp/~styorio/