| Project/Area Number |
17K05350
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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 |
Foundations of mathematics/Applied mathematics
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| Research Institution | Hosei University |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | モデル理論 / ジェネリック構造 / 安定性理論 / 数学基礎論 |
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| Outline of Final Research Achievements |
There exists some famous conjecture which says that if the number of countable models of a theory is finite and not one then the theory is unstable. If there exists a counter-example of the conjecture,it must have a special type. We construct a non omega-categorical theory with a special type, modifying some known example.
Holographic structures are similar to omega-categorical structures. There exists a holographic structure that is not omega-categorical. This example is constructed from a field structure. So the following problem naturally arises: Is there a non omega-categorical holographic structure in which no field is definable? We give a positive answer to the problem using generic construction.
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| Academic Significance and Societal Importance of the Research Achievements |
Lachlan予想はモデル理論においてよく知られた予想であるが，約５０年前のものであり，現在はこの予想を研究対象にしている研究者は少ない．しかし，モデル理論の発展とともに新たな道具が開発されており，この古い予想にうまく適用できるのではないかと考えた．まだ研究は半ばであるが，少しずつ解決に近づいていると考える．
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