Research activity information

• Dividing and forking in random hypergraphs

  Hirotaka Kikyo, Akito Tsuboi

  Elsevier BV, Feb. 2025, Annals of Pure and Applied Logic, 176(2) (2), 103521 - 103521, English

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• Random structures and automorphisms with a single orbit

  Hirotaka Kikyo, Akito Tsuboi

  Abstract We investigate the class of m-hypergraphs whose substructures with l elements have more than sm-element subsets that do not form a hyperedge. The class will have the free amalgamation property if s is small, but it does not if s is large. We find the boundary of s. Suppose the class has the free amalgamation property. In the case $$m \ge 3$$, we demonstrate that the random structure for the class has continuum-many automorphisms with a single orbit. The situation differs from the case of Henson graphs. In the case of generic hypergraphs constructed by Hrushovski’s method using a predimension function, we also demonstrate that they have no automorphisms with a single orbit.

  Springer Science and Business Media LLC, Oct. 2024, Archive for Mathematical Logic, English

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• On the Structure of Hrushovski's Pseudoplanes Associated to Irrational Numbers

  Hirotaka Kikyo

  Apr. 2023, Kokyuroku of RIMS, 2249, 83 - 96, English

  Research institution


• Some remarks on groups definable in certain generic structures

  Hirotaka Kikyo

  May 2022, Kokyuroku of RIMS, 2218, 64 - 70, English

  International conference proceedings


• On the automorphism groups of Hrushovski's pseudoplanes associated to small rational numbers

  Hirotaka Kikyo

  Sep. 2020, Kokyuroku of RIMS, 2170, 26 - 42, English

  Research institution


• On the automorphism group of a Hrushovski's pseudoplane associated to 5/8

  KIKYO Hirotaka

  Jul. 2019, RIMS Kokyuroku, 2119, 75 - 86, English

  Symposium


• On Hrushovski's pseudoplanes

  KIKYO HIROTAKA, OKABE SHUNSUKE

  Let x be a real number with 3/5 < x < 2/3 and M a Hrushovski's pseudoplane associated to x. If x is rational then the theory of M is countably categorical and model complete. If the boundary function is bounded then the theory of M is not model complete. I x is a quadratic irrational then the Hrushovski's boundary function is bounded.

  World Scientific, Jan. 2019, Proceedings of the 14th and 15th Asian Logic Conferences, 175 - 194, English

  [Refereed]

  International conference proceedings


• Model Completeness of the theory of Hrushovski's pseudoplane associated to 5/8

  KIKYO HIROTAKA

  Hrushovski’s pseudoplane associated to rational number 5/8 has a model complete theory.

  RIMS, Kyoto University, Aug. 2018, Kokyuroku of RIMS, Kyoto University, 2084, 29 - 38, English

  Symposium


• Balanced zero-sum sequences and minimal intrinsic extensions

  KIKYO HIROTAKA

  A notion of a balnaced sequence associated to a rational number is defined. For any rational number, a basic balanced sequence s exists. Any rotation of s^k is balanced. Conversely, any balanced sequence is a rotation of s^k for some k.

  RIMS, Kyoto University, Aug. 2018, Kokyuroku of RIMS, Kyoto University, 2079, 54 - 60, English

  Symposium


• Model completeness of generic graphs in rational cases

  Hirotaka Kikyo

  Springer New York LLC, Dec. 2017, Archive for Mathematical Logic, 57, 1 - 26, English

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• Köhler theory for countable quadruple systems

  Hirotaka Kikyo, Masanori Sawa

  2017, Tsukuba Journal of Mathematics, 41(2) (2), 189 - 213, English

  [Refereed]

  Scientific journal


• On K_f in irrational cases

  KIKYO HIROTAKA

  Consider an ab initio amalgamation class K_f with an unbounded increasing concave function f. We conjecture that if K_f has the free amalgamation property then the generic structure for K_f has a model complete theory. We consider the case where the predimension function has an irrational coefficient. We show some statements which seem to be useful to show our conjecture.

  Research Institute for Mathematical Sciences, Kyoto University, Jul. 2016, RIMS Kokyuroku, 2002, 48 - 53, English

  Scientific journal


• Model Complete Generic Graphs I

  KIKYO HIROTAKA

  Let f be a monotone increasing unbounded function which is convex upwards and satisfying some mild condition. Suppose a predimension function has a coefficient 1/2. Then a generic structure for K_f of finite graphs has a model complete theory.

  京都大学数理解析研究所, Apr. 2015, RIMS Kokyuroku, 1938, 15 - 25, English

  Symposium


• Model complete generic structures

  KIKYO HIROTAKA, IKEDA KOICHIRO

  Generic structures constructed from a certain kind of amalgamation classes are shown to have a model complete countably categorical theory.

  World Scientific, Mar. 2015, Proceedings of the 13th Asian Logic Conference, 114 - 123, English

  [Refereed][Invited]

  International conference proceedings


• On superstable generic structures

  Koichiro Ikeda, Hirotaka Kikyo

  Aug. 2012, ARCHIVE FOR MATHEMATICAL LOGIC, 51(5-6) (5-6), 591 - 600, English

  [Refereed]

  Scientific journal


• Model theory of automorphisms

  Kikyo Hirotaka

  The Mathematical Society of Japan, Apr. 2012, SUGAKU, 64(2) (2), 153 - 165, Japanese


• Kolmogorov complexity and characteristic constants of formal theories of arithmetic

  Shingo Ibuka, Makoto Kikuchi, Hirotaka Kikyo

  Oct. 2011, MATHEMATICAL LOGIC QUARTERLY, 57(5) (5), 470 - 473, English

  [Refereed]

  Scientific journal


• On generic automorphisms of a tree structure

  Kikyo, Hirotaka

  Oct. 2010, Kokyuroku of RIMS, Kyoto Univeristy, 1718巻 52-57, English

  Scientific journal


• ON GENERIC STRUCTURES WITH A STRONG AMALGAMATION PROPERTY

  Koichiro Ikeda, Hirotaka Kikyo, Akito Tsuboi

  Sep. 2009, JOURNAL OF SYMBOLIC LOGIC, 74(3) (3), 721 - 733, English

  [Refereed]

  Scientific journal


• Quantifier elimination for lexicographic products of ordered abelian groups

  Kikyo, Hirotaka, Ibuka, Shingo, Tanaka, Hiroshi

  Jun. 2009, Tsukuba Journal of Mathematics, Vol.33, No.1, 95-129(1) (1), 95 - 129, English

  [Refereed]

  Scientific journal


• On the Amalgamation Property for Automorphisms

  Hirotaka Kikyo

  Jun. 2008, The Kokyuroku of RIMS, 1602巻93-102頁, English

  Scientific journal


• On central gap numbers of symmetric groups

  Kikyo Hirotaka

  g(G) denotes the central gap number of a group G. Weshow that for n ≥ 8, g(Sn) ≥ n and g(An) ≥ n-2. We give exact values of g(Sn) and g(An) for small n's. In particular, g(S9) = 9 and g(A9) = 7. Therefore, for any positive integer n ≠ 1, 3, 5 there is a group G such that n = g(G). G can be finite or infinite.

  Department of Mathematics, Faculty of Science, Okayama University, Jan. 2008, Mathematical Journal of Okayama University, 50巻 63-84頁(1) (1), English

  [Refereed]

  Scientific journal


• On Characteristic Constants of Theories Defined by Kolmogorov Complexity

  Shingo Ibuka, Makoto Kikuchi, Hirotaka Kikyo

  2008, Logic, Language, Information and Computation: WoLLIC 2008 Proceedings (Lecture Notes in Computer Science), 5110, 218 - 225, English

  [Refereed]

  In book


• On generic predicates and the amalgamation property for automorphisms

  KIKYO Hirotaka

  Apr. 2005, Proceedings of the School of Science, Tokai University, 40, 19-24, English

  [Refereed]

  Scientific journal


• On predimensions of finite structures

  KIKYO, Hirotaka

  2005, Kokyuroku of RIMS, Kyoto University, 1450, 75-82, English

  Scientific journal


• On generic predicates and automorphisms

  KIKYO Hirotaka

  Kyoto University, 2004, 数理解析研究所講究録, 1390, 1-8, 1 - 8, English

  Scientific journal


• 差分パズル

  桔梗 宏孝, 板井 昌典, 大矢 建正, 花澤 正純

  2003, 東海大学教育研究所紀要, 10, 1-14, Japanese

  [Refereed]

  Scientific journal


• PAPAをもたない理論

  桔梗 宏孝, 坪井 明人, Ehud Hrushovski

  京都大学, 2003, 数理解析研究所講究録, 1344, 11-15, 11 - 15, Japanese

  Scientific journal


• The strict order property and generic automorphisms

  H Kikyo, S Shelah

  Lead, Mar. 2002, JOURNAL OF SYMBOLIC LOGIC, 67(1) (1), 214 - 216, English

  [Refereed]

  Scientific journal


• The definable multiplicity property and generic automorphisms

  Hirotaka Kikyo, Anand Pillay

  Lead, Elsevier, Dec. 2000, Annals of Pure and Applied Logic, 106(1-3) (1-3), 263 - 273, English

  [Refereed]

  Scientific journal


• Model companions of theories with an automorphism

  Hirotaka Kikyo

  Lead, Association for Symbolic Logic, 2000, Journal of Symbolic Logic, 65(3) (3), 1215 - 1222, English

  [Refereed]

  Scientific journal


• On the Groups with Homogeneous Theory

  Hirotaka Kikyo

  Oct. 1998, Tsukuba Journal of Mathematics, 22(2) (2), 551 - 557, English

  [Refereed]

  Scientific journal


• ON REDUCTION PROPERTIES

  H KIKYO, A TSUBOI

  Sep. 1994, JOURNAL OF SYMBOLIC LOGIC, 59(3) (3), 900 - 911, English

  [Refereed]

  Scientific journal


• STRONGLY NONMULTIDIMENSIONAL THEORIES

  H KIKYO

  Jan. 1991, JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 43(1) (1), 203 - 212, English

  [Refereed]

  Scientific journal


• A graph model for probabilistic computation

  Hirotaka Kikyo, Shinichi Yamada

  Dec. 1989, Journal of Information Processing, 12(3) (3), 261 - 265, English

  [Refereed]

  Scientific journal


• Remarks on Zilber's results: On the simplicity of the representation of groups and rings

  Hirotaka Kikyo

  Jan. 1988, Tsukuba Journal of Mathematics, 12(1) (1), 235 - 240, English

  [Refereed]

  Scientific journal

• Model Theory of Automorphisms

  KIKYO HIROTAKA

  A differential field is a field together with a formal differential operator, and a difference field a field together with an automorphism of the field. There is a notion of a differentially closed field analogous to the notion of an algebraically closed field as well as a notion of a difference closed field. Differentially closed fields and difference closed fields can be defi

  American Mathematical Society, Jun. 2016, Sugaku Expositions, 29(1) (1), 1 - 15, English

  [Refereed]

  Introduction scientific journal


• AN UNSATURATED GENERIC STRUCTURE (Model theoretic aspects of the notion of independence and dimension)

  IKEDA KOICHIRO, KIKYO HIROTAKA

  Kyoto University, May 2011, RIMS Kokyuroku, 1741, 9 - 12, English


• On generic automorphisms of a tree structure (New developments of independence notions in model theory)

  Kikyo Hirotaka, Tsuboi Akito

  Kyoto University, Oct. 2010, RIMS Kokyuroku, 1718, 52 - 57, English


• On the Amalgamation Property for Automorphisms (Model theoretic techniques for constructing infinite structures)

  Kikyo Hirotaka

  Kyoto University, Jun. 2008, RIMS Kokyuroku, 1602, 93 - 102, English


• ベクトル空間のGeneric 自己同型(モデル理論における独立概念と次元)

  桔梗 宏孝

  京都大学, May 2007, 数理解析研究所講究録, 1555, 49 - 56, Japanese


• On Predimensions of Finite Structures (Zariski Geometry and Arithmetic Geometry)

  Kikyo Hirotaka

  Kyoto University, Sep. 2005, RIMS Kokyuroku, 1450, 75 - 82, English


• ACFAとManin-Mumford予想 (幾何学的モデル理論の研究)

  桔梗 宏孝

  京都大学, Sep. 2002, 数理解析研究所講究録, 1283, 21 - 26, Japanese


• 複素多様体のモデル理論 (モデル理論とその応用)

  桔梗 宏孝

  京都大学, Jun. 2001, 数理解析研究所講究録, 1213, 55 - 61, Japanese


• 不安定構造のGeneric自己同型写像 (モデル理論とその応用)

  桔梗 宏孝

  京都大学, Jun. 2001, 数理解析研究所講究録, 1213, 19 - 27, Japanese

• 数理解析研究所講究録2249「モデル理論における独立概念と次元の研究」

  Joint editor, 京都大学数理解析研究所, Apr. 2023


• RIMS Kokyuroku 2218, Model theoretic aspects of the notion of independence and dimension

  Hirotaka Kikyo

  Editor, Research Institute for Mathematical Sciences, Kyoto University2, May 2022


• RIMS Kokyuroku 2119 Model Theoretic Aspects of the Notion of Independence and Dimension

  Hirotaka Kikyo

  Editor, Research Institute for Mathematical Sciences, Kyoto University, Jul. 2019


• RIMS Kokyuroku 2002, Model theoretic aspects of the notion of independence and dimension

  KIKYO HIROTAKA

  Editor, Research Institute for Mathematical Sciences, Kyoto University, Jul. 2016, English, This is a proceedings of the RIMS Meeting "Model theoretic aspects of the notion of independence and dimension" held at RIMS, December 14-16, 2015.

  Scholarly book


• Proceedings of the 10th Asian Logic Conference, Kobe, Japan, 1-6 September 2008

  Asian Logic Conference, 新井, 敏康, Brendle, J. (Jörg), 桔梗, 宏孝, Chong, Chi-Tat, Downey, R. G. (Rod G.), 冯, 琦, 小野, 寛晰

  Joint editor, World Scientific, 2010, English, ISBN: 9789814293013


• 岩波 数学辞典 第4版

  Kikyo, Hirotaka

  Contributor, 岩波書店, Mar. 2007, Japanese

  Scholarly book


• 一階の構造のgeneric自己同型写像の研究とその代数学への応用 平成16年度～平成18年度科学研究費補助金(基盤研究(C))研究成果報告書

  Kikyo, Hirotaka

  Single work, 日本学術振興会, Feb. 2007, Japanese

  Scholarly book


• 情報システムと情報技術事典

  Kikyo, Hirotaka

  Contributor, 培風館, Jun. 2006, Japanese

  Scholarly book


• A LOGICAL APPROACH TO DISCRETE MATH

  GRIES, David, SCHNEIDER, Fred B, NANBA, Kanji, DOI, Norihisa, 飯島 正, 小野寺 民也, 桔梗 宏孝, 志村 立矢, 高橋 真

  Joint translation, 日本評論社, Jul. 2001, Japanese

  Others


• 応用論理

  桔梗, 宏孝

  Single work, 共立出版, Mar. 1996, Japanese, ISBN: 4320026519

• On random hypergraphs and automorphisms with a single orbit

  Hirotaka Kikyo

  The Annual Meeting of the Mathematical Society of Japan, 2024, Mar. 2024, Japanese

  Oral presentation


• On automorphisms with a single orbit on random structures

  RIMS共同研究（公開型）「モデル理論における独立概念と次元の研究」, Dec. 2023, English

  Oral presentation


• On cyclic automorphisms

  Hirotaka Kikyo

  The Fall Meeting of the Mathematical Society of Japan, 2023, Sep. 2023, Japanese, Domestic conference

  Oral presentation


• On the structure of Hrushovski's pseudoplanes

  Hirotaka Kikyo

  The Annual Meeting of the Mathematical Society of Japan, 2023, Mar. 2023, Japanese

  Oral presentation


• On Hrushovski's pseudoplanes with irrational dimensions

  Hirotaka Kikyo

  Model theoretic aspects of the notion of independence and dimension (RIMS Symposia), Dec. 2022, English

  Oral presentation


• On generic structures defined with log-like functions

  桔梗 宏孝

  The Fall Meeting of the Mathematical Society of Japan, 2022, Sep. 2022, Japanese

  Oral presentation


• On model completeness of certain generic structures

  桔梗 宏孝

  The Annual Meeting of the Mathematical Society of Japan, 2022, Mar. 2022, Japanese

  Oral presentation


• Some remarks on groups definable in certain generic structures

  Hirotaka Kikyo

  Model theoretic aspects of the notion of independence and dimension (RIMS Symposia), Dec. 2021, English

  Oral presentation


• On model completeness of Hrushovski's pseudoplanes

  Hirotaka Kikyo

  The Annual Meeting of the Mathematical Society of Japan, 2021, Mar. 2021, Japanese

  Oral presentation


• On model completeness of Hrushovski's pseudoplanes in all cases

  Hirotaka Kikyo

  Model theoretic aspects of the notion of independence and dimension, Dec. 2020, English

  Oral presentation


• On Hrushovski's pseudoplanes

  Hirotaka Kikyo

  2019 RIMS Model Theory Workshop, Dec. 2019, English

  Oral presentation


• 有理数係数のHrushovskiの擬平面について

  桔梗 宏孝

  2019日本数学会秋季総合分科会, Sep. 2019, Japanese

  Oral presentation


• On automorphism groups of Hrushovski's pseudoplanes in rational cases

  Hirotaka Kikyo

  Logic Collquium 2019, Aug. 2019, English

  Oral presentation


• On automorphism groups of Hrushovski's pseudoplanes in rational cases

  Hirotaka Kikyo

  Model Theory Workshop in Shanghai 2019, May 2019, English

  [Invited]

  Invited oral presentation


• On automorphism groups of Hrushovski's pseudoplanes

  Hirotaka Kikyo

  RIMS Model Theory Workshop 2018, Dec. 2018, English

  Oral presentation


• Hrushovskiのab initio融合クラスについて

  桔梗 宏孝

  2018日本数学会年会, Mar. 2018, Japanese

  Oral presentation


• On automorphism groups of generic structures

  Hirotaka Kikyo

  2017 RIMS Model Theory Workshop, Dec. 2017, English

  Oral presentation


• クラスK_fについて

  桔梗 宏孝

  2017日本数学会秋季総合分科会, Sep. 2017, Japanese

  Oral presentation


• Structures obtained by Hrushovski's construction and their automorphism groups

  Hirotaka Kikyo

  JCCA 2017, Aug. 2017, Japanese

  [Invited]

  Invited oral presentation


• Model completeness of generic graphs in rational cases

  Hirotaka Kikyo

  The 15th Asian Logic Conference, Jul. 2017, English

  Oral presentation


• On generic structures and their automorphism groups

  Hirotaka Kikyo

  Shanghai Model Theory Workshop 2017, May 2017, English

  [Invited]

  Invited oral presentation


• K_fのジェネリック構造の自己同型群の単純性について

  桔梗 宏孝

  2017日本数学会年会, Mar. 2017, Japanese

  Oral presentation


• On model completeness of generic graphs: Irrational coefficient case

  KIKYO HIROTAKA

  ２０１５年度日本数学会秋季総合分科会, Oct. 2015, Japanese, 京都産業大学（京都府・京都市）, 有理数係数の場合のK_fのジェネリックグラフのモデル完全性の証明で構成したtwigにより、無理数係数の場合には極小固有拡大を構成できることを示した。, Domestic conference

  Oral presentation


• Model complete generic structures II

  KIKYO HIROTAKA, IKEDA KOICHIRO

  Annual Meeting of the Mathematical Society of Japan 2014, Mar. 2014, Japanese, Gakushuin University, We consider hyper-graphs with 3-hyper-edges. Let A be such a hyper-graph. Let δ(A) = |A|- e(A) where e(A) is the number of hyper-edges in A. Suppose A is a hyper-subgraph of C. If A ⊊ X ⊆ C implies δ(A) < δ(X), then we write A < C. Let f(x) = log3(x + 1). Let Kf = {A | B ⊆ A ⇒ δ(B) ≧ f(|B|)}. Then the theory of the generic structure of (Kf ;<) is model complete. More generally,, Domestic conference

  Oral presentation


• Model complete generic structures I

  IKEDA KOICHIRO, KIKYO HIROTAKA

  Annual Meeting of the Mathematical Society of Japan 2014, Mar. 2014, Japanese, Gakushuin University, In 1988, Hrushovski constructed new strongly minimal generic structure to give a counterexample to the Zilber conjecture. In his paper, Hrushovski pointed out that the theory of his structure is nearly model complete. In this talk, we give a characterization of model completeness in generic structures. Using the characterization, we want to consider model completeness of Hrusho, Domestic conference

  Oral presentation


• On 0-extensions in generic constructions

  KIKYO HIROTAKA

  The 13th Asian Logic Conference, Sep. 2013, English, Sun Yat-Sen University (Guangzhou City, China), We discuss how to construct 0-extensions in amalgamation classes in abundance. There are many small structures with certain properties so that we can combine them to make 0-extensions. We also discuss their applications., International conference

  [Invited]

  Invited oral presentation


• On superstable generic structures

  Hirotaka Kikyo

  The 12th Asian Logic Conference, Dec. 2011, English, Victoria University of Wellington, International conference

  Oral presentation


• Superstable generic structures

  Hirotaka Kikyo, 池田 宏一郎

  2011 Fall Meeting of the Mathematical Society of Japan, Sep. 2011, Japanese, 日本数学会, Shinshu University, Domestic conference

  Oral presentation


• Unsaturated generic structures II

  Kikyo, Hirotaka

  RIMS Meeting: Model theoretic aspects of the notion of independence and dimension, Dec. 2010, English, 京都大学数理解析研究所, Research Institute of Mathematical Sciences, Kyoto University, International conference

  Oral presentation


• On imitation of generic structures

  Kikyo, Hirotaka

  The Fall Meeting of the Mathematical Society of Japan, 2010, Sep. 2010, Japanese, (社) 日本数学会, Nagoya University, Domestic conference

  Oral presentation


• Ab Initio Generic Structures and Saturation

  Kikyo, Hirotaka

  Model Theory Summer School 2010, Aug. 2010, Japanese, Seitoku University, Domestic conference

  Oral presentation


• On generic automorphisms and the strict order property

  Hirotaka Kikyo

  Logic Colloquium 2010, Jul. 2010, English

  Oral presentation


• On model companions of an automorphism

  Kikyo, Hirotaka

  2010 Annual Meeting of the Mathematical Society of Japan, Mar. 2010, Japanese, 日本数学会, Keio University, Yagami Campus, Domestic conference

  [Invited]

  Invited oral presentation


• On model companions of an automorphism

  Kikyo, Hirotaka

  Model Theory Kirishima 2010 New developments of "independence" in model theory, Mar. 2010, English, 京都大学数理解析研究所, Ryokojin-Sanso, Kirishima, International conference

  Oral presentation


• On instability and a class of automorphisms

  Kikyo, Hirotaka, Tsuboi, Akito

  2009 Fall Meeting of the Mathematical Society of Japan, Sep. 2009, Japanese, 日本数学会, Osaka University, Toyonaka Campus, Domestic conference

  Oral presentation


• Instability and Generic Automorphisms

  Kikyo, Hirotaka

  Logicum Urbanae Lugduni, Jul. 2009, English, Universite Lyon 1, Universite Lyon 1, Lyon, France, International conference

  Invited oral presentation


• On direct products of ordered abelian groups

  Hirotaka Kikyo

  Annual Meeting of the Mathematical Society of Japan, Mar. 2009, Japanese, 日本数学会, The University of Tokyo, Komaba Campus, Domestic conference

  Oral presentation


• On generic automorphisms of unstable structures

  Hirotaka Kikyo

  Model Theory Meeting in Kagoshima, Feb. 2009, Japanese, Kagoshima International University, Domestic conference

  Oral presentation


• On Characteristic Constants of Theories Defined by Kolmogorov Complexity

  Shingo Ibuka, Hirotaka Kikyo, Makoto Kikuchi

  Fall Meeting of the Mathematical Society of Japan, Sep. 2008, Japanese, 日本数学会, Tokyo Institute of Technology, Domestic conference

  Oral presentation


• On Characteristic Constants of Theories Defined by Kolmogorov Complexity

  Shingo Ibuka, Makoto Kikuchi, Hirotaka Kikyo

  15th International Workshop, WoLLIC 2008, Jul. 2008, English, Helliot-Watt University, Edinburgh, UK, International conference

  Oral presentation


• On the AE-axiomatization of generic structures

  Hirotaka Kikyo

  Around the Classification Theory Workshop, Jun. 2008, English, Leeds University, UK, Leeds University, UK, International conference

  Invited oral presentation


• On the amalgamation property for automorphisms

  Ikeda, Koichiro, Kikyo, Hirotaka

  Annual Meeting of the Mathematical Society of Japan, Mar. 2008, Japanese, 日本数学会, Kinki University, Domestic conference

  Oral presentation


• The rationality of local zeta functions and the uniformity in degrees

  Kikyo, Hirotaka

  A study of real algebraic geometry in weakly o-minimal structures, Mar. 2008, Japanese, 京都大学数理解析研究所, Research Institute for Mathematical Sciences, Domestic conference

  Oral presentation


• On the amalgamation property for automorphisms

  Kikyo, Hirotaka

  RIMS Workshop: Model theoretic techniques for constructing infinite structures, Nov. 2007, Japanese, 京都大学数理解析研究所, Research Institute for Mathematical Sciences, Domestic conference

  Oral presentation


• On amalgamation property for automorphisms

  Kikyo, Hirotaka

  International Workshop on Model Theory, Nov. 2007, English, Yonsei University, Yonsei University, South Korea, International conference

  Invited oral presentation


• Direct products of ordered abelian groups and quantifier elimination

  Kikyo, Hirotaka, Ibuka, Shingo, Tanaka, Hiroshi

  Fall Meeting of the Mathematical Society of Japan, Sep. 2007, Japanese, Tohoku University, Domestic conference

  Oral presentation


• Products of ordered abelian groups and quantifier elimination

  Kikyo, Hirotaka, Ibuka, Shingo, Tanaka, Hiroshi

  Workshop: Model Theory Summer School 2007, Aug. 2007, English, University of Tsukuba, Domestic conference

  Oral presentation


• Generic automorphisms of a vector space

  Hirotaka Kikyo

  RIMS Meeting "Model theoretic aspects of the notion of independence and dimension", Nov. 2006, Japanese, 京都大学数理解析研究所, Research Institute in Mathematical Sciences, Kyoto University, Domestic conference

  Oral presentation


• Additive predimension and a strong amalgamation property

  Hirotaka Kikyo

  Fall meeting of the Mathematical Society of Japan, Sep. 2006, Japanese, the Mathematical Society of Japan, School of Science, Osaka City University, Domestic conference

  Oral presentation


• Pseudo-finite fields and the amalgamation property for automorphisms

  Hirotaka Kikyo

  Model Theory Summer School 2006, Aug. 2006, Japanese, Tokai University, Yoyogi Campus, Domestic conference

  Oral presentation


• On generic automorphisms of modular structures

  KIKYO Hirotaka

  Annual Meeting of the Mathematical Society of Japan, Mar. 2006, Japanese, 日本数学会, Chuo University, Domestic conference

  Oral presentation


• On generic structure with certain amalgamation property

  KIKYO Hirotaka

  日本数学会秋季総合分科会, Sep. 2005, Japanese, 日本数学会, Okayama University, Domestic conference

  Oral presentation


• On p-adic numbers

  KIKYO Hirotaka

  RIMS Meeting: On first order definability in a non-standard model of the arithmetic, Sep. 2005, Japanese, 京都大学数理解析研究所, Research Institute for Mathematical Sciences, Domestic conference

  Oral presentation


• Strongly minimal structure

  KIKYO Hirotaka

  Summer School in Mathematical Logic 2005, Aug. 2005, Japanese, Hosei University, Ichigaya Campus, Domestic conference

  Oral presentation


• あるgeneric構造の公理について

  桔梗 宏孝

  日本数学会2005年度年会, 2005, Japanese, 日本数学会, 日本大学理工, Domestic conference

  Oral presentation


• genericな述語と自己同型

  桔梗 宏孝

  日本数学会2004年度年会, 2004, Japanese, 日本数学会, 筑波大学, Domestic conference

  Oral presentation


• 対称群のcentral gap number について

  桔梗 宏孝

  日本数学会2003年度秋季総合分科会, 2003, Japanese, 日本数学会, 千葉大学, Domestic conference

  Oral presentation


• PAPAをもたない理論

  桔梗 宏孝, 坪井 明人, Ehud Hrushovski

  京都大学数理解析研究所「モデル理論と代数幾何の交流」共同研究集会, 2003, Japanese, 京都大学数理解析研究所, 未記入, Domestic conference

  Oral presentation


• generic構造上のgeneric自己同型について

  桔梗 宏孝

  京都大学数理解析研究所「Generic構造とその応用」共同研究集会, 2003, Japanese, 京都大学数理解析研究所, 未記入, Domestic conference

  Oral presentation


• A Theory without PAPA

  桔梗 宏孝, 坪井 明人, Ehud Hrushovski

  日本数学会2003年度年会, 2003, English, 日本数学会, 東京大学, Domestic conference

  Oral presentation


• Generic Automorphisms and the DMP

  Hirotaka Kikyo

  Logic Colloquium 2000, Jul. 2000

  Oral presentation

• 日本ソフトウェア科学会


• 情報処理学会


• 日本数学会


• Association for Symbolic Logic

• Study of generic structures and their automorphism groups

  Kikyo Hirotaka

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Kobe University, Apr. 2017 - Mar. 2020, Principal investigator

  Hrushovski defined a class of finite graphs depending on a parameter whose value is a real number between 0 and 1. Each class has a limit which is a countably infinite structure, called a generic structure. It is highly homogeneous in some sense. There are variants due to Wagner. Hrushovski's original structures are not variants due to Wagner. In case that the parameter is a rational number, we showed that the elementary theory of the generic structure is model complete in both cases. Also, we showed that the automorphism group of the generic structure is a simple group if the parameter is a rational number. If the parameter is a usual irrational number then the theory of the generic structure is not model complete. The proplems are still open if the parameter is a general irrational number.


• A study on new construction in model theory

  IKEDA Koichiro, TSUBOI Akito, KIKYO Hirotaka, BALDWIN John T, WAGNER Frank O.

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Hosei University, 01 Apr. 2014 - 31 Mar. 2017

  The purpose of this study was to improve the Hrushovski construction. Then I proved that every generic structure had near model completeness. On the other hand, there are some generic structures whose theories are not model complete. I obtained a characterization of model completeness in generic structures. Moreover, I proved that any generic structure with the full amalgamation was always stable.


• Study on generic structures in model theory

  Kikyo Hirotaka, IKEDA Koichiro, TSUBOI Akito

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Kobe University, Apr. 2013 - Mar. 2016

  Consider graphs or hypergraphs as structures. We define a dimension of a structure by the number of points - α× the number of edges. With this dimension, we can define a closed substructure. Given a class of finite structures with some property, we can construct a structure called a generic structure by gluing together these structures. A generic structure reflects closed structure relations between finite structures in the given class. There is a class denoted Kf defined with a boundary function f. If α is a rational number, the generic structure will be model complete under some assumption on f. We have some important lemmas in case that α is irrational. There is a notion of the full amalgamation property. If a class has the full amalgamation property then the generic structure can be axiomatised by universal existential sentences. We constructed an infinite projective plane such that it has no finite projective plane as a substructure.


• A study of a new method of construction in model theory

  IKEDA Koichiro, TSUBOI Akito, KIKYO Hirotaka

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Hosei University, 2011 - 2013

  Baldwin's conjecture states that any stable generic structure is strictly stable or omega-stable. For this conjecture, I proved that there was no generic structure whose theory was strictly superstable. This result means that the conjecture is solved negatively. I also proved that if a stable generic structure was saturated, then it was strictly stable or omega-stable. Evans and Wang showed that an omega-categorical generic structure did not have SOP_4. To generalize their result, Baldwin and I proved that a saturated generic structure did not have SOP_4. We also gave an example of a generic structure which was saturated but not omega-categorical. I had studied the model completeness of generic structures in cooperation with Kikyo, and then we proved that Hrushovski's simple omega-categorical generic structure was model complete.


• A Study of the Model Theory of Random Graphs

  IKEDA Koichiro, TSUBOI Akito, KIKYO Hirotaka

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Hosei University, 2007 - 2009

  Our aim is to study generic structures as a generalization of random graphs, and moreover to construct a counter-example of Lachlan conjecture using the generic construction. One of our results is a theorem which gave a solution of Baldwin's problem. Another is a theorem which proved that it was difficult to construct a counter-example of Lachlan conjecture using the generic construction.


• Study of first order model theory and its application

  TSUBOI Akito, IKEDA Kazuma, SAKAI Ko, IKEDA Koichiro, KIKYO Hirotaka, SHIOYA Masahiro

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), University of Tsukuba, 2007 - 2009

  We extended Steinhorn's omitting types theorem. His theorem holds when the theory T is superstable. We weakened the assumption of superstablity to a weaker condition of supersimlicity. Steinhorn's original proof uses the notion of average types. Our proof does not use such a notion. First we proved a quite general result and then, by applying the result to a model of supersimple theory, we get the following extension of Steinhorn's result as a corollary : The result : Let L be a countable language and T a complete supersimple theory formulated in L. Let M be a countable model of Thaving an infinite independent (in the sense of forking) set. Suppose that M omits a complete type p over the empty set. Then there is a proper elementary extension N of M that also omits p.


• Study of existentially closed models and its applications

  KIKYO Hirotaka, ITAI Masanori, TSUBOI Akito, IKEDA Koichiro

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Kobe University, 2007 - 2009

  The existence condition for real solution of a quadratic equation can be written by a simple inequality on coefficients. This property is generalized to a property called QE. We clarified when a product of ordered abelian groups has QE. There are Baldwin-Shelah generic structures corresponding to random graphs. We proved that the statements valid in such a structure can be axiomatized by conditions of a simple form. Even with the existence of an infinite order, if we specify the restriction of an automorphism to a fixed small model, then we found an example where the class of generic automorphisms is elementary.


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

  KIKYO Hirotaka, ITAI Masanori, WATANABE Junzo, TSUBOI Akito

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), 2004 - 2006

  1. The amalgamation property for automorphisms is preserved under the addition of generic predicates to a theory. Therefore, if we get an unstable theory by the addition of generic predicates to a stable theory, then the class of the generic automorphisms of the resulting theory is not elementary. 2. The omega-power of the additive group of the rational numbers equipped with a shift function is a quasi-minimal structure. Its theory can be axiomatized by sentences expressing a kind of genericity. Let K be a field. The class of generic automorphisms of an infinite K-vector space is elementary. Its theory can be axiomatized in the same manner as above. Z-power of a countable infinite K-vector space equipped with a shift function is a quasi-minimal model of this theory. It is omega-stable with Morley rank omega. 3. Consider a typical predimension function on the finite structures for a finite relational language and the class of finite structures in which the empty set is closed with respect to this predimension. Then the generic structure of this class has a universal-existential theory. This is a rather general solution to a problem of Baldwin-Shelah. 4. If a model N of PA is definable without parameters in an elementary extension M of the structure of natural numbers and N and M are elementarily equivalent, then N is definably isomorphic to M. But if we allow N to be definable with parameters then there are examples such that M and N are elementarily equivalent but non-isomorphic, or M and N are isomorphic but not definably isomorphic. 5. For graded Artinian K-algebras, we gave several characterizations of the strong and weak Lefschetz Properties. With these results, we found new classes of complete intersections with the strong Lefschetz Property.


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

  TSUBOI Akito, MOTOHASHI Nobuyoshi, SHIOYA Masahiro, ITAI Masanori, KIKYO Hirotaka

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), University of Tsukuba, 2003 - 2005

  The notion of generic structure is obtained by generalizing the construction of random graphs. This can be done as follows. Let K be a class of finite structure. We assume there is a dimension function δ on K. We also assume that with respect to δ,K has the amalgamation property. Then by amalgamating structures in K rather randomly, we can get an inifinite (countable) strurture. This infinite structure M is called a K-generic structure. M is characterize by the following two properties (1)every finite substructure of M is isomorphic to a member in K, (2)If A


• Simplicity and Amalgamation in Model Theory

  TSUBOI Akito, TSUKADA Nobutaka, SHIOYA Masahiro, MOTOHASHI Nobuyoshi, KIKYO Hirotaka, NISHIMURA Hirokazu

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Institute of Mathematics, University of Tsukuba, 2001 - 2002

  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,


• Applications of Frobenius map to Commutative Ring Theory and Algebraic Geometry

  WATANABE Keiichi, ITAI Masanori, WATANABE Junzo, MATSUURA Yutaka, SUZUKI Masahiko, MORI Makoto

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B), 1995 - 1997

  1 Characterization of Singularities in Characteristic 0 via Frobenius endomorphism. We found that log-terminal singularity and F-regular rings are equivalent notions in the case the ring is Q-Gorenstein. The same is true for rational singularities and F-rational rings. 2 By definig F-terminal rings, the terminal singularities are characterized in 3-dimensional case. F-terminal and Q-Gorenstein imply terminal singularity in any dimension. But in dimension 4, unfortunately, there is a counterexample to the converse and F-rational ring is characterized by the property that its general hyperplane section is F-rational in Gorenstein case. 3 The characterization of regular local rings by Hilbert-Kunz multiplicity=1.Namely, an unmixed local ring of characteristic p is regular if and only if its H-K multiplicity is 1. Also we succeeded to classify the 2-dimensional rings with Hibert-Kunz multiplicity less than 9/4.


• 確率過程の調和モデルによる研究

  和泉澤 正隆, 中村 昭宏, 桔梗 宏孝, 藤井 信彦, 郡山 彬, 氏家 勝巳

  日本学術振興会, 科学研究費助成事業, 一般研究(C), 東海大学, 1994 - 1994

  本研究は、調和解析、特に、Hardy空間論における特異積分作用素とマルチンゲ-ル変換との対応による確率過程の構造追求、ならびに、具体的なモデルの構築と検討・解析による確率過程の特徴付けを行うことを目的とした。そして、確率過程の変形状況の直接的な研究結果までには至らなかったが、 1.藤井により、作用素の評価に関する次の新たな結果が得られた。 特異積分作用素やmaximal functionに関連してL^Pノルムやweek typeの評価を行うとき、一般に、二つの作用素の積についてはもとと同じ形の評価での有界性がいえるとは限らない。しかしながら、作用素の有界性が要求されるのはcube上、すなわち、局所的なものであることに注目し解析した。n次元実空間上のコンパクトな台をもつ局所可積分関数に対して各cube上である作用素に関するweek typeの不等式が成立する、さらに、それよりL^Pノルム不等式が得られることが示された。 2.氏家により、確率モデルの構築の探求と統計的な意味付けの考察により、次の新たな結果が得られた。 四次元正規分布に従う確率変数の象限確率(つまり全ての要素成分が正である確率)は、その統計的手法に対する重要性・必要性が認識されながらも、計算方法は複雑であり困難であった。しかるに、その数値計算を可能にする方法、ならびに、それを用いた尤度比検定統計量の下側確率や最尤推定量の計算方法を導いた。なお、この結果は第17回Biometric国際会議[94年8月、カナダ、オンタリオ於]で氏家氏ほか工藤昭夫氏、山本義郎氏の共同発表研究結果とも一部重複しているものである。


• 数学的構造における決定手続きの研究

  〓梗 宏孝, 花沢 正純, 成嶋 弘, 楢崎 隆, 岩田 茂樹, 和泉澤 正隆

  日本学術振興会, 科学研究費助成事業, 一般研究(C), 東海大学, 1993 - 1993

  本年度は,構造とその中である述語で定義される部分構造との関係を中心に研究を行なった.L-構造Mがあるとする.Lに一変数述語PがあるときN=M^Pを考えるとNは自然にL^-=L＼{P}構造になる.ここで,Nの中の関係が外側のMの中で定義されるとすると,それはすでにNの中で定義されているという状況を考える.このときMはN上reduction propertyをもつという.この性質を厳密に定義しようとすると何通りかの定義が考えられる.そこで,O-reduction property,reduction property,strong reduction property,uniform reduction propertyという性質を提唱し,これらの性質の相互関係を調べ,またこれらの条件のもとでNの性質がどの程度Mに移るかを調べた.Mの理論が安定の場合はO-reduction propertyがstrong reduction propertyを除いて最も強く,reduction propertyとuniform reduction propertyが同値になる.一般にはstrong reduction propertyからreduction propertyが導かれるが,他のものは独立な性質になることが分かった.Mが可算モデルのとき,その理論がP上極小でstrong reduction propertyをもつならばNの〓_0-範疇性はMに移る.0-reduction propertyしか成り立たない場合には,構造を増やしてこの反例に拡張する一般的方法を与えた.さらに,Mの理論TがP上極小でuniform reduction propertyをもつ場合,Nの理論T^-が〓-安定ならばTもそうなり,また単次元性も移ることを示した.O-reduction propertyだけある場合は,上と同様に反例に拡張できる. 他に,非決定性と交代Turing機械の間の関係,n×n盤上のオセロゲームの計算量の決定,ジャンプナンバー問題に関する研究などを行なった.


• 数え上げ組合せ論の鎖数の研究

  成嶋 弘, 桔梗 宏孝, 土屋 守正, 郡山 彬, 渡辺 敬一, 花沢 正純

  日本学術振興会, 科学研究費助成事業, 一般研究(C), 東海大学, 1992 - 1992

  1.系統分類学における、ある分岐図のもとでの仮想的形質状態の復元問題を、組合せ論的最適化問題として定式化し、“meclian interval(中間区間)"の概念の導入と再帰的定式化により、この問題に対する一般的解法を与えた。この解法の計算量の考察や系統分類学上の他の問題の解決への手がかりも得られた。これら系統分類学上の問題を扱うことによって、数え上げ組合せ論に新しい研究分野が開かれ、他の分野との関連によってダイナミックに進展するものと思われる。 2.上の解法は最節約復元順序集合の構造決定や、NPー完全問題の研究に重要な示唆を与えるものと思われる。 3.順序集合論におけるジャンプナンバー問題(JNP)はNPー完全な問題として知られているが、この問題に対するニューラルネットワークを用いた解法を与えた。この問題は教授法ににおける教授順序の最適性に関する問題にも関連している。 4.グラフの順序構造の研究において、ボンド束とグラフそれぞれの性質の間の関係が明確に示された。また、グラフの反鎖交数の研究が進展した。 5.その他、問題を視覚化するための研究道具の開発を行った。複累力学系の細部の構造(順序構造等を含む)を研究するためのデータ作成を、ユーザの負担にならぬように、できるかぎり自動化するソフトウェアを開発した。 6.可換代数とのいくつかの関連も得られた。


• Intersection Graphの研究

  土屋 守正, 岩田 茂樹, 桔梗 宏孝, 和泉澤 正隆, 渡辺 敬一, 成嶋 弘

  日本学術振興会, 科学研究費助成事業, 一般研究(C), 東海大学, 1991 - 1991

  Antichain Intersection number Wai(G)がWai(G)=【symmetry】:^tccofg{1【symmetry】1+1i(【symmetry】)}(i(()SY.sym.〔))={S(V)1^〓u【thermodynamics】V;S(V)≦S(u)})とtotal Clique Cover【symmetry】を用いてとらえられることがわかった。この結果を用いて,2ーcell embedable graph Gに対して,Wai(G)≦(1ー1/(X(G^*)))・IV(G^*)1であり,平面グラフに対して,Wai(G)≦4/3(IVG)1ー2)であり,極大平面的グラフに対して,Wai(G)≦IV(G)1ー2という評価が得られている。ここで,G^*はGの双対グラフのことであり、X(G^*)はG^*は染色数のことである。さらに,Kaーfree,rーregular graph G(IV(G)≧4,r≧3)に対して,Wai(G)=Wm(G)+IEs(G)1であるとこも前述の結果より得られている。ただし,Wm(G)=【symmetry】:^tccofGl【symmetry】1であり,Es(G)={U,V}∈E(G)|N(u)ー{V}=N(V)ー{u } }である。また,一般の正則グラフに対しては,2ー正則グラフGに対して,Wai(G)=IE(G)|,3ー正則グラフGに対して,Wai(G)=3角形に含まれないGの辺の本数+Gの三角形の個数,であることが得られ,4,5ー正則グラフに対しても同様の結果が得られた。 Wai(Kn+Ne)を求めるために,Intersecting familyに関するテクニックを応用しようとしたことがら派生した結果として,最小元(1)を持つposetpに関するshifted complex FとFの交差部分剤yに対して,1y1≦#{F∈F;(1)∈F}なることが得られた。 W(G)を決定することがNP完全であることがS.Poljak等によって得られていることがわかり,Wai(G)及びWui(G)を決定することについてもNP完全であることが予想され目下このことについて研究中である。さらに,uniform intersection number Wui(G)をtotal clique coverからとらえることについても研究中である。