9 found
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  1.  33
    The Strict Order Property and Generic Automorphisms.Hirotaka Kikyo & Saharon Shelah - 2002 - Journal of Symbolic Logic 67 (1):214-216.
    If T is a model complete theory with the strict order property, then the theory of the models of T with an automorphism has no model companion.
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  2.  13
    The Definable Multiplicity Property and Generic Automorphisms.Hirotaka Kikyo & Anand Pillay - 2000 - Annals of Pure and Applied Logic 106 (1-3):263-273.
    Let T be a strongly minimal theory with quantifier elimination. We show that the class of existentially closed models of T{“σ is an automorphism”} is an elementary class if and only if T has the definable multiplicity property, as long as T is a finite cover of a strongly minimal theory which does have the definable multiplicity property. We obtain cleaner results working with several automorphisms, and prove: the class of existentially closed models of T{“σi is an automorphism”: i=1,2} is (...)
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  3.  15
    Model Companions of Theories with an Automorphism.Hirotaka Kikyo - 2000 - Journal of Symbolic Logic 65 (3):1215-1222.
    For a theory T in L, T σ is the theory of the models of T with an automorphism σ. If T is an unstable model complete theory without the independence property, then T σ has no model companion. If T is an unstable model complete theory and T σ has the amalgamation property, then T σ has no model companion. If T is model complete and has the fcp, then T σ has no model completion.
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  4.  13
    On Generic Structures with a Strong Amalgamation Property.Koichiro Ikeda, Hirotaka Kikyo & Akito Tsuboi - 2009 - Journal of Symbolic Logic 74 (3):721-733.
    Let L be a finite relational language and α=(αR:R ∈ L) a tuple with 0 < αR ≤1 for each R ∈ L. Consider a dimension function $ \delta _\alpha (A) = \left| A \right| - \sum\limits_{R \in L} {\alpha {\mathop{\rm Re}\nolimits} R(A)} $ where each eR(A) is the number of realizations of R in A. Let $K_\alpha $ be the class of finite structures A such that $\delta _\alpha (X) \ge 0$ 0 for any substructure X of A. We (...)
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  5.  30
    On Reduction Properties.Hirotaka Kikyo & Akito Tsuboi - 1994 - Journal of Symbolic Logic 59 (3):900-911.
  6.  9
    Kolmogorov Complexity and Characteristic Constants of Formal Theories of Arithmetic.Shingo Ibuka, Makoto Kikuchi & Hirotaka Kikyo - 2011 - Mathematical Logic Quarterly 57 (5):470-473.
    We investigate two constants cT and rT, introduced by Chaitin and Raatikainen respectively, defined for each recursively axiomatizable consistent theory T and universal Turing machine used to determine Kolmogorov complexity. Raatikainen argued that cT does not represent the complexity of T and found that for two theories S and T, one can always find a universal Turing machine such that equation image. We prove the following are equivalent: equation image for some universal Turing machine, equation image for some universal Turing (...)
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  7. Kolmogorov Complexity and Characteristic Constants of Formal Theories of Arithmetic.Shingo Ibuka, Masato Kikuchi & Hirotaka Kikyo - 2011 - Mathematical Logic Quarterly 57 (5):470-473.
     
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  8.  4
    On Superstable Generic Structures.Koichiro Ikeda & Hirotaka Kikyo - 2012 - Archive for Mathematical Logic 51 (5-6):591-600.
    We construct an ab initio generic structure for a predimension function with a positive rational coefficient less than or equal to 1 which is unsaturated and has a superstable non-ω-stable theory.
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  9.  6
    Model Completeness of Generic Graphs in Rational Cases.Hirotaka Kikyo - 2018 - Archive for Mathematical Logic 57 (7-8):769-794.
    Let \ be an ab initio amalgamation class with an unbounded increasing concave function f. We show that if the predimension function has a rational coefficient and f satisfies a certain assumption then the generic structure of \ has a model complete theory.
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