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Simplicity and Amalgamation in Model Theory

Research Project

Project/Area Number 13640099
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionInstitute of Mathematics, University of Tsukuba

Principal Investigator

TSUBOI Akito  Institute of Mathematics, Associate Professor, 数学系, 助教授 (30180045)

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)
Project Period (FY) 2001 – 2002
Project Status Completed (Fiscal Year 2002)
Budget Amount *help
¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 2002: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 2001: ¥1,800,000 (Direct Cost: ¥1,800,000)
KeywordsModel Theory / Simple Theory / Peano Arithmetic / 単純性
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,

Report

(3 results)
  • 2002 Annual Research Report   Final Research Report Summary
  • 2001 Annual Research Report
  • Research Products

    (16 results)

All Other

All Publications (16 results)

  • [Publications] Akito Tsuboi, M.Murakami: "Expanding the additive reduct of a model of Peano arithmetic"MLQ. 49,3. (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Akito Tsuboi: "Random Amalgamation of Simple Theories"Math. Log. Quart.. 47,1. 45-50 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Masahiro Shioya: "Generating the club filter on $P_\kappa\lambda$"Topology and its Applications. 122. 415-419 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H.Kikyo, S.Shelah: "The strict order property and generic automorphisms"J. Symbolic Logic. 67,1. 214-216 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Akito Tsuboi, M. Murakami: "Expanding the additive reduct of a model of Peano arithmetic"MLQ. 49. 3 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Akito Tsuboi: "Random Amalgamation of Simple Theories"Math, Log. Quart.. 47. 1,45-50 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Masahiro Shioya: "Generating the club filter on $P_\kappa\ lambda$"Topology and its Applications. 122. 415-419 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H. Kikyo, S. Shelah: "The strict order property and generic automorphisms"J. Symbolic Logic. 67 No. 1. 214-216 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Akito TSUBOI, Masahiko MURAKAMI: "Expanding the additive reduct of a model of peano arithmatic"MLQ. 49・3(to appear). (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] A.TSUBOI, N.TSUKADA: "A real vector space which has an norm but which has no inner products"Proc. of the 36th MLG meeting. 38-39 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Masahiro SHIOYA: "Generating the club filter on P_xλ"Topology and its Applications. 122. 415-419 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] H.Kikyo, S.Shelah: "The strict order property and generic automorphisms"J. Symb. Log. 67・1. 214-216 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 坪 井 明 人(Akito Tsuboi): "Random Amalgamation of Simple Theories"Math. Log. Quart.. 47. 45-50 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] S.Shelah., Akito Tsuboi: "Definability of Initial Segments"(submitted).

    • Related Report
      2001 Annual Research Report
  • [Publications] Hirokazu Nishimura: "Synthetic Differential Geometry of Jet Bundles"Bull. Belg. Math. Soc. 8. 639-650 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Masahiro Shioya: "Generating the club filter on P_k(λ)"Topology and Its Application. (to appear).

    • Related Report
      2001 Annual Research Report

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Published: 2001-04-01   Modified: 2016-04-21  

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