Project/Area Number |
17K05350
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Foundations of mathematics/Applied mathematics
|
Research Institution | Hosei University |
Principal Investigator |
|
Project Period (FY) |
2017-04-01 – 2020-03-31
|
Project Status |
Completed (Fiscal Year 2019)
|
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)
|
Keywords | モデル理論 / ジェネリック構造 / 安定性理論 / 数学基礎論 |
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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