| Budget Amount *help |
¥2,300,000 (Direct Cost: ¥2,300,000)
Fiscal Year 2006: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2005: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2004: ¥900,000 (Direct Cost: ¥900,000)
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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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