2006 Fiscal Year Final Research Report Summary
A research on generic constructions
| Project/Area Number |
16540123
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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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 |
IKEDA Koichiro Hosei University, Faculty of Business Administration, Associate Professor (60332029)
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| Project Period (FY) |
2004 – 2006
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| Keywords | generic structure / stability theory / model theory / Lachlan's conjecture / random graph / omega-stable / superstable |
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| Research Abstract |
The aim of this project was to get a clue to a solution of the following two problems :
Lachlan's conjecture : For any stable theory T, the number of countable models of T is one or infinite.
Baldwin's problem : Is any superstable generic structure omega-stable?
In 2004, I obtained a partial result of Lachlan's conjecture. The result was presented in Model theory summer meeting at Tokai University Seminar House. In March 2005, I got a partial result of Baldwin's problem. The result was published in Kokyuroku of RIMS. After that I got the following theorem : There is no generic saturated graph that is superstable but omega-stable. The result was presented in Logic Colloquium 2005, and published in Journal of Mathematical Society of Japan. In September 2005, I got the following theorem : If K is closed under quasi-substructures, then there is no generic saturated structures that is superstable but omega-stable. The result was another version of the above theorem.
This was published in Kokyukoku of RIMS. On the other hand, I discussed axioms for generic structures with Kikyo and Tsuboi. As a result, we got the following theorem : For any real number alpha, a K_alpha-generic structure is AE-axiomatizable. The result was presented in Nihon sugakkai in September 2006, and is submitted.
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Research Products
(39 results)
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[Presentation] 加法的局所次元と強い融合性2006
Author(s)
池田 宏一郎, 桔梗 宏孝, 坪井 明人
Organizer
日本数学会秋季総合分科会
Place of Presentation
大阪市大
Year and Date
20060900
Description
「研究成果報告書概要(和文)」より
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