Model Theory of analytic structures and quasi-minimal fields

• Project/Area Number: 19540146
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Tokai University
• Principal Investigator: ITAI Masanori Tokai University, 理学部, 教授 (80266361)
• Project Period (FY): 2007 – 2009
• Project Status: Completed (Fiscal Year 2009)
• Budget Amount: ¥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)
• 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

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.

Research Products

• [Journal Article] 解析的ザリスキー構造とChowの定理 (2008)
  • Author(s): 板井昌典
  • Journal Title: 数理解析研究所講究録 1602巻 Pages: 64-69
• [Journal Article] 解析的ザリスキー構造とChowの定理 (2008)
  • Author(s): 板井 昌典
  • Journal Title: 京都大学数理解析研究所 講究録 1602 Pages: 64-69
• [Journal Article] 解析的ザリスキー構造とHrushovski generic構造 (2007)
  • Author(s): 板井昌典
  • Journal Title: 数理解析研究所講究録 1574巻 Pages: 39-49
• [Journal Article] 非代数的ザリスキー幾何 (2007)
  • Author(s): 板井昌典
  • Journal Title: 数理解析研究所講究録 1555巻 Pages: 40-48
• [Journal Article] 非代数的ザリスキー幾何 (2007)
  • Author(s): 板井 昌典
  • Journal Title: 京都大学数理解析研究所 講究録 1555 Pages: 40-48
• [Journal Article] 解析的ザリスキー構造と Hrushovski generic 構造 (2007)
  • Author(s): 板井 昌典
  • Journal Title: 京都大学数理解析研究所 講究録 1574 Pages: 39-49
• [Presentation] Model Theory of analytic Zariski structures (2010)
  • Author(s): 板井昌典
  • Organizer: 日本数学会2010年度年会
  • Place of Presentation: 慶応大学
  • Year and Date: 2010-03-24
• [Presentation] Model Theory of analytic Zariski structures (2010)
  • Author(s): 板井昌典
  • Organizer: 日本数学会2010年度年会
  • Place of Presentation: 慶応大学矢上キャンパス
  • Year and Date: 2010-03-24
• [Presentation] Model Theory of analytic Zariski structures (2010)
  • Author(s): 板井昌典
  • Organizer: Model Theory Kirishima 2010
  • Place of Presentation: 霧島
  • Year and Date: 2010-03-05
• [Presentation] Model Theory of analytic Zariski structures (2010)
  • Author(s): 板井昌典
  • Organizer: Model Theory Kirishima 2010
  • Place of Presentation: 鹿児島県霧島市旅行人山荘
  • Year and Date: 2010-03-05
• [Presentation] Kexにおける「解析集合」の構造に関する注意 (2009)
  • Author(s): 板井昌典
  • Organizer: 日本数学会2009年度年会
  • Place of Presentation: 東京大学
  • Year and Date: 2009-06-26
• [Presentation] Kex における「解析集合」の構造に関する注意 (2009)
  • Author(s): 板井 昌典
  • Organizer: 日本数学会年会
  • Place of Presentation: 東京大学駒場キャンパス
  • Year and Date: 2009-03-26
• [Presentation] Analytic Zariski structures and a generalized Chow Theorem (2008)
  • Author(s): 板井昌典
  • Place of Presentation: 近畿大学
  • Year and Date: 2008-03-26
• [Presentation] Analytic Zariski structures and a generalized Chow Theorem (2008)
  • Author(s): 板井 昌典
  • Organizer: 日本数学会年会
  • Place of Presentation: 近畿大学本部キャンパス
  • Year and Date: 2008-03-26