2002 Fiscal Year Final Research Report Summary
Simplicity and Amalgamation in Model Theory
| Project/Area Number |
13640099
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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 | Institute of Mathematics, University of Tsukuba |
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Principal Investigator |
TSUBOI Akito Institute of Mathematics, Associate Professor, 数学系, 助教授 (30180045)
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| Co-Investigator(Kenkyū-buntansha) |
TSUKADA Nobutaka Institute of Mathematics, Assistant Professor, 数学系, 助手 (50015559)
SHIOYA Masahiro Institute of Mathematics, Lecturer, 数学系, 講師 (30251028)
MOTOHASHI Nobuyoshi Institute of Mathematics, Professor, 数学系, 教授 (70015874)
KIKYO Hirotaka Tokai University, Department of Natural Science, Associate Professor, 理学部, 助教授 (80204824)
NISHIMURA Hirokazu Institute of Mathematics, Lecturer, 数学系, 講師 (70135614)
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| Project Period (FY) |
2001 – 2002
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| Keywords | Model Theory / Simple Theory / Peano Arithmetic |
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| Research Abstract |
Let M be a model of PA and l≠ω be an initial segment of M. Let L_0 be the language for additive ordered groups.
Then, there is a model N of PA such that
(a) M＼L_0 = N＼L_0,
(b) x ・^M x = x ・^N x if and only if x ・^M ∈xI.
If I is closed under ・^M the second condition can be replaced by
2'. x ・^M x = x ・^N x if and only if x ∈ I,
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