2009 Fiscal Year Final Research Report
Study of existentially closed models and its applications
| Project/Area Number |
19540126
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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 | Kobe University |
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Principal Investigator |
KIKYO Hirotaka Kobe University, 大学院・工学研究科, 教授 (80204824)
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| Co-Investigator(Renkei-kenkyūsha) |
ITAI Masanori 東海大学, 理学部, 教授 (80266361)
TSUBOI Akito 筑波大学, 大学院・数理物質科学研究科, 教授 (30180045)
IKEDA Koichiro 法政大学, 経営学部, 教授 (60332029)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 存在閉モデル / モデル完全 / 存在記号の消去 / ジェネリック構造 / 自己同型 / 順序構造 / 木構造 / 順序加群 |
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| Research Abstract |
The existence condition for real solution of a quadratic equation can be written by a simple inequality on coefficients. This property is generalized to a property called QE. We clarified when a product of ordered abelian groups has QE. There are Baldwin-Shelah generic structures corresponding to random graphs. We proved that the statements valid in such a structure can be axiomatized by conditions of a simple form. Even with the existence of an infinite order, if we specify the restriction of an automorphism to a fixed small model, then we found an example where the class of generic automorphisms is elementary.
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