ITAI Masanori 板井昌典

Researcher Number	80266361
Other IDs
Affiliation (based on the past Project Information) *help	2004 – 2009: 東海大学, 理学部, 教授 2005: Tokai University, Department of Natural Science, Professor, 理学部・情報数理学科, 教授 2003 – 2004: 東海大学, 理学部情報数理学科, 教授 1996 – 1999: 東海大学, 理学部, 助教授
Review Section/Research Field	Principal Investigator General mathematics (including Probability theory/Statistical mathematics) Except Principal Investigator General mathematics (including Probability theory/Statistical mathematics) / 教科教育 / Algebra
Keywords	Principal Investigator 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 Except Principal Investigator generic structure … More / ジェネリック構造 / Frobenius map / rational singularity / F-rational ring / complete intersection / Peano Arithmetic / definable model / Lefschetz Property / 数学教育 / 数学史 / 数学教育方法 / 数学教育法 / 存在閉モデル / モデル完全 / 存在記号の消去 / 自己同型 / 順序構造 / 木構造 / 順序加群 / 自己同型写像 / 初等クラス / ランダムグラフ / 順序群 / 辞書式順序積 / 理論の公理化 / 関係構造 / 任意存在形の公理 / コルモゴロフ複雑性 / モデル完全性 / commutative ring theory (可挽環論) / algebraic geometry (代数幾何学) / singularities (特異点論) / 有理特異点 / terminal singularity / 例外因子 / Hilbert-Kunz重複度 / Frobenius写像 / regular local ring / Hilbert-Kung multiplicity / 特異点の解消 / (例外因子の)discropanciy / terninal singularity / F-teruinal ring / test ideal / geometric genus / GNentein ring / F-terminal ring / canonical singularity / log-terminal singularity / F-regular ring / Algebraic Geometry / Singularities / Terminal Singularity / regular ring / Hilbert-Kunz multiplicity / 有限モデル / 公理系 / 公理化 / 自然数 / モデル / ペアノ公理系 / 再帰的 / 同型 / 定義可能 / モデル理論 / 安定性 / タイリング / finite model / axiom / axiomatizability / generic自己同型 / generic述語 / generic構造 / 融合性 / ペアノ算術 / 定義可能モデル / Lefschetz性 / Artinian Gorenstein Algebra / central gap number / symmetric group / 局所次元 / 自由融合性 / 不安定 / 加群の自己同型 / quasi-minimal structure / generic automorphism / generic predicate / amalgamation property Less

Study of existentially closed models and its applications
- Principal Investigator
  
  KIKYO Hirotaka
- Project Period (FY)
  2007 – 2009
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  General mathematics (including Probability theory/Statistical mathematics)
- Research Institution
  Kobe University
Model Theory of analytic structures and quasi-minimal fieldsPrincipal Investigator
- Principal Investigator
  
  ITAI Masanori
- Project Period (FY)
  2007 – 2009
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  General mathematics (including Probability theory/Statistical mathematics)
- Research Institution
  Tokai University
Research of generic automorphisms of first order structures and its application to algebra
- Principal Investigator
  
  KIKYO Hirotaka
- Project Period (FY)
  2004 – 2006
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  General mathematics (including Probability theory/Statistical mathematics)
- Research Institution
  Kobe University
  Tokai University
Infinite Method in Finite Model Theory and its application for aiming to solve Lachlan's conjecture.
- Principal Investigator
  
  TSUBOI Akito
- Project Period (FY)
  2003 – 2005
- Research Category
  
  Grant-in-Aid for Scientific Research (C)
- Research Field
  
  General mathematics (including Probability theory/Statistical mathematics)
- Research Institution
  University of Tsukuba
数学史を用いた高校数学教育システムの開発
- Principal Investigator
  
  平野葉一
- Project Period (FY)
  1997 – 1999
- Research Category
  
  Grant-in-Aid for Exploratory Research
- Research Field
  
  教科教育
- Research Institution
  Tokai University
Applications of Frobenius map to Commutative Ring Theory and Algebraic Geometry
- Principal Investigator
  
  WATANABE Keiichi
- Project Period (FY)
  1995 – 1997
- Research Category
  
  Grant-in-Aid for Scientific Research (B)
- Research Field
  
  Algebra
- Research Institution
  NIHON UNIVERSITY
  Tokai University

All 2010 2009 2008 2007 2005 2004

All Journal Article Presentation

[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
- Data Source
  KAKENHI-PROJECT-19540146
[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
- Data Source
  KAKENHI-PROJECT-19540146
[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
- Data Source
  KAKENHI-PROJECT-19540146
[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
- Data Source
  KAKENHI-PROJECT-19540146
[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
- Data Source
  KAKENHI-PROJECT-19540146
[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
  
  Pages: 40-48
- Data Source
  KAKENHI-PROJECT-19540126
[Journal Article] 解析的ザリスキー構造とChowの定理2007
- Author(s)
  板井昌典
- Journal Title
  
  数理解析研究所講究録 1602
  
  Pages: 64-69
- Data Source
  KAKENHI-PROJECT-19540126
[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
- Data Source
  KAKENHI-PROJECT-19540146
[Journal Article] ω-saturated quasi-minimal models of Th(Q^ω, +, σ, O),2005
- Author(s)
  Masanori Itai, Kentaro Wakai
- Journal Title
  
  Mathematical Logic Quarterly, 51・3
  
  Pages: 258-262
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-15540104
[Journal Article] Omega-saturated quasi- minimal models of Th (Q^ω,+,σ,0)2005
- Author(s)
  Masanori Itai, Kentaro Wakai
- Journal Title
  
  Mathematical Logic Quarterly 51-3
  
  Pages: 258-262
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-16540117
[Journal Article] Omega-saturated quasi-minimal model of Th(Q^omega, +, sigma,0)2005
- Author(s)
  Masanori Itai, et al.
- Journal Title
  
  Mathematical Logic Quarterly 51・3
  
  Pages: 258-262
- Data Source
  KAKENHI-PROJECT-16540117
[Journal Article] Omega-saturated quasi-minimal models of Th(Q^ω, +, σ, 0)2005
- Author(s)
  Masanori Itai
- Journal Title
  
  Mathematical Logic Quarterly Vol.51, No.3
  
  Pages: 258-262
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-16540117
[Journal Article] ω-saturated quasi-minimal models of Th(Q^ω,+,σ,0),2005
- Author(s)
  Masanori Itai, Kentaro Wakai
- Journal Title
  
  Mathematical Logic Quarterly 51・3
  
  Pages: 258-262
- Data Source
  KAKENHI-PROJECT-15540104
[Journal Article] ω-saturated quasi-minimal models of Th(Q^ω,+,σ,0),2005
- Author(s)
  Masanori Itai, Kentaro Wakai
- Journal Title
  
  MLQ vol 51, no3
  
  Pages: 258-262
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-15540104
[Journal Article] Omega-saturated quasi-minimal model of Th(Q^-omega,+,sigma,0)2005
- Author(s)
  Masanori Itai
- Journal Title
  
  Mathematical Logic Quarterly Vol.51, No.3
  
  Pages: 258-262
- Data Source
  KAKENHI-PROJECT-16540117
[Journal Article] Construction of saturated quasi-minimal structures,2004
- Author(s)
  Masanori Itai, Kentaro Wakai, Akito Tsuboi
- Journal Title
  
  The journal of symbolic logic Volume 69, Issue 1,
  
  Pages: 9-22
- Description
  「研究成果報告書概要(和文)」より
- Data Source
  KAKENHI-PROJECT-15540104
[Journal Article] Construction of saturated quasi-minimal structure.2004
- Author(s)
  Masanori Itai, Akito Tsuboi, Kentaro Wakai
- Journal Title
  
  The Journal of Symbolic Logic 69・1
  
  Pages: 9-22
- Data Source
  KAKENHI-PROJECT-15540104
[Journal Article] Construction of Saturated Quasi-minimal Structure2004
- Author(s)
  Masanori Itai, et al.
- Journal Title
  
  The Journal of Symbolic Logic 69・1
  
  Pages: 9-22
- Data Source
  KAKENHI-PROJECT-16540117
[Journal Article] Construction of saturated quasi-minimal structures2004
- Author(s)
  Masanori Itai, Kentaro Wakai, Akito Tsuboi
- Journal Title
  
  The journal of symbolic logic volume 69, Issue 1
  
  Pages: 9-22
- Description
  「研究成果報告書概要(欧文)」より
- Data Source
  KAKENHI-PROJECT-15540104
[Presentation] Model theory of analytic Zariski structures2010
- Author(s)
  M. Itai
- Organizer
  Model theory Kirishima 2010, 京都大学RIMS合宿型セミナー
- Place of Presentation
  旅行人山荘(霧島)
- Year and Date
  2010-03-05
- Data Source
  KAKENHI-PROJECT-19540126
[Presentation] Model Theory of analytic Zariski structures2010
- 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
- Data Source
  KAKENHI-PROJECT-19540146
[Presentation] Model Theory of analytic Zariski structures2010
- Author(s)
  板井昌典
- Organizer
  Model Theory Kirishima 2010
- Place of Presentation
  霧島
- Year and Date
  2010-03-05
- Data Source
  KAKENHI-PROJECT-19540146
[Presentation] Model theory of analytic Zariski structures2010
- Author(s)
  M. Itai
- Organizer
  2010日本数学会年会
- Place of Presentation
  慶應義塾大学
- Year and Date
  2010-03-24
- Data Source
  KAKENHI-PROJECT-19540126
[Presentation] Model Theory of analytic Zariski structures2010
- 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
- Data Source
  KAKENHI-PROJECT-19540146
[Presentation] Model Theory of analytic Zariski structures2010
- 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
- Data Source
  KAKENHI-PROJECT-19540146
[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
- Data Source
  KAKENHI-PROJECT-19540146
[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
- Data Source
  KAKENHI-PROJECT-19540146
[Presentation] Analytic Zariski structures and a generalized Chow Theorem2008
- Author(s)
  板井昌典
- Place of Presentation
  近畿大学
- Year and Date
  2008-03-26
- Data Source
  KAKENHI-PROJECT-19540146
[Presentation] Analytic Zariski structures and a generalized Chow Theorem2008
- 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
- Data Source
  KAKENHI-PROJECT-19540146

1. KIKYO Hirotaka (80204824)

# of Collaborated Projects: 4 results

# of Collaborated Products: 0 results
2. TSUBOI Akito (30180045)

# of Collaborated Projects: 4 results

# of Collaborated Products: 3 results
3. WATANABE Junzo (40022727)

# of Collaborated Projects: 2 results

# of Collaborated Products: 0 results
4. IKEDA Koichiro (60332029)

# of Collaborated Projects: 2 results

# of Collaborated Products: 0 results
5. WATANABE Keiichi (10087083)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
6. MATSUURA Yutaka (50096905)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
7. SUZUKI Masahiko (00171249)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
8. MORI Makoto (60092532)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
9. MOTOHASHI Nobuyoshi (70015874)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
10. SHIOYA Masahiro (30251028)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
11. 平野葉一 (20189856)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
12. 河村勝久 (70119668)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
13. 中村義作 (20109200)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
14. 秋山仁 (00096942)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
15. 堀江邦明 (20201759)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
16. 太田雅巳 (40025490)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
17. 原正雄 (10238165)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
18. 土屋守正 (00188583)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
19. 和泉澤正隆 (50108445)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results
20. 内村桂輔 (20092835)

# of Collaborated Projects: 1 results

# of Collaborated Products: 0 results

ITAI Masanori 板井 昌典

Research Projects

Research Products

Co-Researchers

Study of existentially closed models and its applications

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Model Theory of analytic structures and quasi-minimal fieldsPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Research of generic automorphisms of first order structures and its application to algebra

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Infinite Method in Finite Model Theory and its application for aiming to solve Lachlan's conjecture.

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

数学史を用いた高校数学教育システムの開発

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

Applications of Frobenius map to Commutative Ring Theory and Algebraic Geometry

Principal Investigator

Project Period (FY)

Research Category

Research Field

Research Institution

[Journal Article] 解析的ザリスキー構造とChowの定理2008

Author(s)

Journal Title

Data Source

[Journal Article] 解析的ザリスキー構造とChowの定理2008

Author(s)

Journal Title

Data Source

[Journal Article] 解析的ザリスキー構造とHrushovski generic構造2007

Author(s)

Journal Title

Data Source

[Journal Article] 非代数的ザリスキー幾何2007

Author(s)

Journal Title

Data Source

[Journal Article] 解析的ザリスキー構造と Hrushovski generic 構造2007

Author(s)

Journal Title

Data Source

[Journal Article] 非代数的ザリスキー幾何2007

Author(s)

Journal Title

Data Source

[Journal Article] 解析的ザリスキー構造とChowの定理2007

Author(s)

Journal Title

Data Source

[Journal Article] 非代数的ザリスキー幾何2007

Author(s)

Journal Title

Data Source

[Journal Article] ω-saturated quasi-minimal models of Th(Q^ω, +, σ, O),2005

Author(s)

Journal Title

Description

Data Source

[Journal Article] Omega-saturated quasi- minimal models of Th (Q^ω,+,σ,0)2005

Author(s)

Journal Title

ITAI Masanori 板井昌典