| Project/Area Number |
23540164
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
|---|
| Research Institution | Hosei University |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Renkei-kenkyūsha) |
TSUBOI Akito 筑波大学, 数理物質科学研究科, 教授 (30180045)
KIKYO Hirotaka 神戸大学, システム情報学研究科, 教授 (80204824)
|
|---|
| Project Period (FY) |
2011 – 2013
|
| Project Status |
Completed (Fiscal Year 2013)
|
| Budget Amount *help |
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
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: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
|
|---|
| Keywords | モデル理論 / 数理論理学 / 数学基礎論 / generic構造 / ジェネリック構造 / Lachlan予想 / 安定性理論 / 超安定 |
|---|
| Research Abstract |
Baldwin's conjecture states that any stable generic structure is strictly stable or omega-stable. For this conjecture, I proved that there was no generic structure whose theory was strictly superstable. This result means that the conjecture is solved negatively. I also proved that if a stable generic structure was saturated, then it was strictly stable or omega-stable.
Evans and Wang showed that an omega-categorical generic structure did not have SOP_4. To generalize their result, Baldwin and I proved that a saturated generic structure did not have SOP_4. We also gave an example of a generic structure which was saturated but not omega-categorical.
I had studied the model completeness of generic structures in cooperation with Kikyo, and then we proved that Hrushovski's simple omega-categorical generic structure was model complete.
|
