Model Theory of analytic structures and quasi-minimal fields
| Project/Area Number |
19540146
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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 | Tokai University |
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Principal Investigator |
ITAI Masanori Tokai University, 理学部, 教授 (80266361)
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| Project Period (FY) |
2007 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | モデル理論 / 解析的構造 / 擬極小体 / 解析的ザリスキー幾何 / 数理論理学 / 解析的ザリスキー構造 / 擬指数関数 / 擬極小構造 / generic 構造 |
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| Research Abstract |
There are two results : the first one is concerning "Chow's Theorem". This famous theorem in algebraic geometry claims that any analytic variety in projective space is in fact algebraically defined. Dr. Peatfield and Prof. Zilber at Oxford University had proved a Chow type theorem in an analytic Zariski structure situation. We proved a generalization of their theorem.
The second one is to apply Richardson's Theorem to algebraically closed fields equipped with a pseudo-exponentiation called Kex. Richardson's theorem gives irreducible decompositions of the zero sets to a system of algebraic-exponential equations. An algebraic-exponential equation is an algebraic equation allowing finitely may exponential functions to appear in it. We proved that the same statement holds in Kex.
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Report
(4 results)
Research Products
(14 results)
