| Project/Area Number |
22540110
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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 筑波大学, 数理物質系, 教授 (30180045)
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| Co-Investigator(Kenkyū-buntansha) |
塩谷 真弘 筑波大学, 数理物質系, 准教授 (30251028)
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| Project Period (FY) |
2010 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | モデル理論 / 安定性理論 / 数理論理学 / ロジック / タイプ / 排除定理 / 定義可能集合 / 構造 / 順序極小 |
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| Research Abstract |
We introduced several new notions concerning indiscernibility of trees. A tree is by definition an ordered set (O,<) such that, for any $a ￥in O$, the initial segment $￥{b ￥in O: b<a￥}$ determined by a is a linearly ordered set.A typical example of tree is the set $￥omega^{<￥omega}$ of finite $￥omega$-sequences with the order relation $<_{￥rm ini}$, where $￥eta <_{￥rm ini} ￥nu$ means that $￥eta$ is a proper initial segment of $￥nu$.In this study, we worked in some structure $M$ in the language $L$. A subset $A$ of the form $(a_￥eta)_{￥eta ￥in O}$, where $O$ is a tree, and $a_￥eta$ is an element in $M$ labeled by $￥eta$, is also called a tree. We studied the indiscernibility of such trees $A$ in general settings and then applied the obtained results to the study of unstable theories. Among others, we proved that if $￥Gamma$ (a set of conditions described by formulas) has the strong subtree property then $￥Gamma$ is realized by a strongly indiscernible tree.
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