2013 Fiscal Year Final Research Report
A study of a new method of construction in model theory
| Project/Area Number |
23540164
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Hosei University |
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Principal Investigator |
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| 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)
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| Project Period (FY) |
2011 – 2013
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| Keywords | モデル理論 / 数理論理学 / 数学基礎論 |
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| 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.
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