| Project/Area Number |
15540104
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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 | University of Tsukuba |
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Principal Investigator |
TSUBOI Akito University of Tsukuba, Graduate school of pure and applied science, Associate Professor, 大学院・数理物質科学研究科, 助教授 (30180045)
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| Co-Investigator(Kenkyū-buntansha) |
MOTOHASHI Nobuyoshi University of Tsukuba, Graduate school of pure and applied science, Professor, 大学院・数理物質科学研究科, 教授 (70015874)
SHIOYA Masahiro University of Tsukuba, Graduate school of pure and applied science, Assistant Professor, 大学院・数理物質科学研究科, 講師 (30251028)
ITAI Masanori Tokai University, Department of Natural Science, Professor, 理学部・情報数理学科, 教授 (80266361)
KIKYO Hirotaka University of Kobe, Department of Technology, Professor, 工学部, 教授 (80204824)
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| Project Period (FY) |
2003 – 2005
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| Project Status |
Completed (Fiscal Year 2005)
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| Budget Amount *help |
¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 2005: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2004: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2003: ¥1,100,000 (Direct Cost: ¥1,100,000)
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| Keywords | generic structure / finite model / axiom / axiomatizability / 自然数 / モデル / ペアノ公理系 / 再帰的 / 同型 / 定義可能 / モデル理論 / 安定性 / タイリング |
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| Research Abstract |
The notion of generic structure is obtained by generalizing the construction of random graphs. This can be done as follows.
Let K be a class of finite structure. We assume there is a dimension function δ on K. We also assume that with respect to δ,K has the amalgamation property. Then by amalgamating structures in K rather randomly, we can get an inifinite (countable) strurture. This infinite structure M is called a K-generic structure. M is characterize by the following two properties (1)every finite substructure of M is isomorphic to a member in K, (2)If A<B in K, and A<M then M has an isomorphic copy of B over A.
The first condition can be stated by sentences but unfortunately the second one cannot be expressed by sentences. This is because, the relation A<M cannot be expressed by a single sentence. We introduced the notion of strong amalgamation property, and prove that if the class K has the strong amalgamation property then the theory of K-generic models is axiomatized. This work is a joint work with Hirotaka Kikyo and Koichiro Ikeda.
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