| Project/Area Number |
18540143
|
|---|
| 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 | Kanagawa University |
|---|
Principal Investigator |
ABE Yoshihiro Kanagawa University, Faculty of Engineering, Professor (10159452)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
KAMO Shizuo University of Osaka Prefecture, Faculty of Science, Professor (30128764)
SHIOYA Masahiro University of Tsukuba, Graduate School of Pure and Applied Sciences, Fulltime Lecturer (30251028)
FUCHINO Sakae Chubu University, Faculty of Engineering, Professor (30292098)
|
|---|
| Project Period (FY) |
2006 – 2007
|
| Project Status |
Completed (Fiscal Year 2007)
|
| Budget Amount *help |
¥1,610,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2006: ¥700,000 (Direct Cost: ¥700,000)
|
|---|
| Keywords | P_κλ / partition property / ineffability / stationary reflection / saturated ideal / fiorcing / club filter / diamond principle / Ρ_κλ / mild ineffability / reflection / 正規極大フィルター |
|---|
| Research Abstract |
(1) We proved that |Pκλ|=λ if κ is mildly λ ineffable and cf(λ)〓κ.
(2) We showed the club filter on Pκλ is weakly presaturated under the Reflection principle.
(3) We showed n is mildly A ineffable Pκ(2^<λ<κ>) has the weak partition property.
(4) We proved every ineffbale subset of Pκλ has the partition property if no cardinal in (κ, λ] is II^2_1-indescribable.
(5) Starting from a model of a huge cardinal we built a simple forcing model in which ω_1 carries an ω_2 saturated ideal.
(6) We extended a theorem of Shelah on the diamond principle in Pω_1λ(◇ω_, λ,) to Pκλ as follows:
(a) ◇_<κ, λ> holds if 2^ω=2^κ with κ<λ
(b) Building upon a model of a supercompact cardinal, we gave a forcing model in which 2^ω=2^κ whereas holds whenever κ< λ.
(7) We got some independence results for cofinality, additivity number, and covering number of the ideal I_f.
|
