Application of the Axiomatic Set Theory to the Infinitary Combinatorics
Grant-in-Aid for Scientific Research (C)
|Allocation Type||Single-year Grants |
General mathematics (including Probability theory/Statistical mathematics)
|Research Institution||Chubu University (2001)|
Kitami Institute of Technology (2000)
FUCHINO Sakae Chubu University, Dept.of Engineering, Professor, 工学部, 教授 (30292098)
MIYAMOTO Tadatoshi Nanzan Univ., Dept.of MS and IT, Ass.Prof., 情報管理学科, 助教授 (70229889)
BRENDLE Jorg Kobe Univ., Grad.School for Sci.and Tech., Ass.Prof., 自然科学研究科, 助教授 (70301851)
TITANI Satoko Chubu University, Dept.of Engineering, Professor, 工学部, 教授 (90207283)
塩谷 真弘 筑波大学, 数学系, 講師 (30251028)
嘉田 勝 北見工業大学, 工学部, 助手 (00312447)
|Project Period (FY)
2000 – 2001
Completed (Fiscal Year 2001)
|Budget Amount *help
¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 2001: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2000: ¥1,100,000 (Direct Cost: ¥1,100,000)
|Keywords||weak Freeese-Nation property / SEP / ideal property / Cohen model / random model / real-valued measurability / club principle / cardinal invariants / maximal almost disjoint family / Heckler real / Blumberg's theorem / OCA / club principle / 強制法 / Solovay model / random実数 / 測度代数 / 可測基数 / 実数値可測基数|
The main subjects of this research project were:
(1)study of the principle asserting that P(ω) has the weak Freese-Nation property (WFN), and its variations;
(2)study of the models of set theory where the continuum has some large cardinal property like real-valued measurability (RVM) or its categorical dual;
(3)other set-theoretic or combinatoric subjects including problems from the set-theory of reals.
Concerning (1), Fuchino and Stefan. Geschke could obtain some fundamental results conserning the property SEP which is a weakening of WFN of P(ω) introduced by I.Juhasz and K.Kunen. Building on a recent result by S.Shelah, Fuchino could reconstruct a theorem by Juhasz, Soukup, Szentmiklossy on the principle C^s(κ) and showed the connections of this principle with variations of WFN of P(ω).
For (2), Puchino and S.Shelah gave a positive answer to a question by David Fremlin whether there is a model of RVM which is different from Solovey's standard model of RVM by some "mathematical" property. The model found Fuchino and Shelah satisfies the club principle for some cardinal -κ, which is not the case for the standard model by Solovey.
Concerning (3), Fuchino together with Stefan Geschke and Lajos Soukup studied some new type of cardinal invariants connected with almost disjoint family of subsets of ω and could obtain some consistency results on these cardinal invariants.
Report (3 results)
Research Products (29 results)