8 found
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  1.  23
    Minimal but Not Strongly Minimal Structures with Arbitrary Finite Dimensions.Koichiro Ikeda - 2001 - Journal of Symbolic Logic 66 (1):117-126.
    An infinite structure is said to be minimal if each of its definable subset is finite or cofinite. Modifying Hrushovski's method we construct minimal, non strongly minimal structures with arbitrary finite dimensions. This answers negatively to a problem posed by B. I Zilber.
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  2.  13
    A Note on Generic Projective Planes.Koichiro Ikeda - 2002 - Notre Dame Journal of Formal Logic 43 (4):249-254.
    Hrushovski constructed an -categorical stable pseudoplane which refuted Lachlan's conjecture. In this note, we show that an -categorical projective plane cannot be constructed by "the Hrushovski method.".
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  3.  7
    On Theories Having Three Countable Models.Koichiro Ikeda, Akito Tsuboi & Anand Pillay - 1998 - Mathematical Logic Quarterly 44 (2):161-166.
    A theory T is called almost [MATHEMATICAL SCRIPT CAPITAL N]0-categorical if for any pure types p1,…,pn there are only finitely many pure types which extend p1 ∪…∪pn. It is shown that if T is an almost [MATHEMATICAL SCRIPT CAPITAL N]0-categorical theory with I = 3, then a dense linear ordering is interpretable in T.
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  4.  6
    A Note on Stability Spectrum of Generic Structures.Yuki Anbo & Koichiro Ikeda - 2010 - Mathematical Logic Quarterly 56 (3):257-261.
    We show that if a class K of finite relational structures is closed under quasi-substructures, then there is no saturated K-generic structure that is superstable but not ω -stable.
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  5.  8
    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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  6.  3
    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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  7.  2
    Ab Initio Generic Structures Which Are Superstable but Not Ω-Stable.Koichiro Ikeda - 2012 - Archive for Mathematical Logic 51 (1-2):203-211.
    Let L be a countable relational language. Baldwin asked whether there is an ab initio generic L-structure which is superstable but not ω-stable. We give a positive answer to his question, and prove that there is no ab initio generic L-structure which is superstable but not ω-stable, if L is finite and the generic is saturated.
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  8.  2
    Almost Total Elementary Maps.Koichiro Ikeda & Akito Tsuboi - 1995 - Mathematical Logic Quarterly 41 (3):353-361.
    A partial map f of a structure M is called almost total if |M — dom| = |M — ran| < ω. We study a difference between an almost total elementary map and an automorphism.
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