30 found
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  1. On the Existence of Indiscernible Trees.Kota Takeuchi & Akito Tsuboi - 2012 - Annals of Pure and Applied Logic 163 (12):1891-1902.
    We introduce several concepts concerning the indiscernibility of trees. A tree is by definition an ordered set such that, for any a∈O, the initial segment {b∈O:b (...)
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  2.  9
    Generalized Amalgamation and N -Simplicity.Byunghan Kim, Alexei S. Kolesnikov & Akito Tsuboi - 2008 - Annals of Pure and Applied Logic 155 (2):97-114.
    We study generalized amalgamation properties in simple theories. We formulate a notion of generalized amalgamation in such a way so that the properties are preserved when we pass from T to Teq or Theq; we provide several equivalent ways of formulating the notion of generalized amalgamation.We define two distinct hierarchies of simple theories characterized by their amalgamation properties; examples are given to show the difference between the hierarchies.
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  3.  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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  4.  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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  5.  7
    A Construction of Real Closed Fields.Yu-Ichi Tanaka & Akito Tsuboi - 2015 - Mathematical Logic Quarterly 61 (3):159-168.
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  6.  9
    On the Number of Independent Orders.Kota Takeuchi & Akito Tsuboi - 2021 - Annals of Pure and Applied Logic 172 (2):102886.
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  7. On the Number of Independent Partitions.Akito Tsuboi - 1985 - Journal of Symbolic Logic 50 (3):809-814.
  8. Proceedings of the 14th and 15th Asian Logic Conferences.Byunghan Kim, Jörg Brendle, Gyesik Lee, Fenrong Liu, R. Ramanujam, Shashi M. Srivastava, Akito Tsuboi & Liang Yu (eds.) - 2019
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  9.  8
    Algebraic Types and Automorphism Groups.Akito Tsuboi - 1993 - Journal of Symbolic Logic 58 (1):232-239.
  10.  24
    Nonstandard Models That Are Definable in Models of Peano Arithmetic.Kazuma Ikeda & Akito Tsuboi - 2007 - Mathematical Logic Quarterly 53 (1):27-37.
    In this paper, we investigate definable models of Peano Arithmetic PA in a model of PA. For any definable model N without parameters in a model M, we show that N is isomorphic to M if M is elementary extension of the standard model and N is elementarily equivalent to M. On the other hand, we show that there is a model M and a definable model N with parameters in M such that N is elementarily equivalent to M but (...)
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  11.  61
    On Theories Having a Finite Number of Nonisomorphic Countable Models.Akito Tsuboi - 1985 - Journal of Symbolic Logic 50 (3):806-808.
  12.  11
    A Note on Stationarity of Types Over Models in Simple Theories.Makoto Kobayashi & Akito Tsuboi - 2008 - Mathematical Logic Quarterly 54 (6):625-628.
    We investigate stationarity of types over models in simple theories. In particular, we show that in simple theories with finite SU-rank, any complete type over a model having Cantor-Bendixson rank is stationary.
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  13.  51
    Construction of Saturated Quasi-Minimal Structure.Masanori Itai, Akito Tsuboi & Kentaro Wakai - 2004 - Journal of Symbolic Logic 69 (1):9-22.
    The notion of quasi-minimal structures was defined by B. Zil'ber as a natural generalization of minimal structures. Inspired by his work, we study here basic model theoretic properties of quasiminimal structures. Main result is the construction of ω-saturated quasi-minimal models under ω-stability assumption.
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  14.  21
    Implicit Definability of Subfields.Akito Tsuboi & Kenji Fukuzaki - 2003 - Notre Dame Journal of Formal Logic 44 (4):217-225.
    We say that a subset A of M is implicitly definable in M if there exists a sentence $\phi$ in the language $\mathcal{L} \cup \{P\}$ such that A is the unique set with $ \models \phi$. We consider implicit definability of subfields of a given field. Among others, we prove the following: $\overline{\mathbb{Q}}$ is not implicitly $\emptyset$-definable in any of its elementary extension $K \succ \overline{\mathbb{Q}}$. $\mathbb{Q}$ is implicitly $\emptyset$-definable in any field K with tr.deg $_{\mathbb{Q}}K < \omega$. In a (...)
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  15.  15
    Strongly 2-Dimensional Theories.Akito Tsuboi - 1988 - Journal of Symbolic Logic 53 (3):931-936.
  16.  3
    Nonstandard Methods for Finite Structures.Akito Tsuboi - 2020 - Mathematical Logic Quarterly 66 (3):367-372.
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  17.  11
    Expanding the Additive Reduct of a Model of Peano Arithmetic.Masahiko Murakami & Akito Tsuboi - 2003 - Mathematical Logic Quarterly 49 (4):363-368.
    Let M be a model of first order Peano arithmetic and I an initial segment of M that is closed under multiplication. LetM0 be the {0, 1,+}-reduct ofM. We show that there is another model N of PA that is also an expansion of M0 such that a · Ma = a · Na if and only if a ∈ I for all a ∈ M.
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  18.  20
    On Definability of Normal Subgroups of a Superstable Group.Akito Tsuboi - 1992 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 38 (1):101-106.
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  19.  21
    Random Amalgamation of Simple Theories.Akito Tsuboi - 2001 - Mathematical Logic Quarterly 47 (1):45-50.
    Let T1 and T2 be two simple complete theories in disjoint languages. We prove that there is a simple complete theory which extends T1 ∪ T2 if T2 has a certain condition.
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  20.  11
    On Interpretability of Almost Linear Orderings.Akito Tsuboi & Kentaro Wakai - 1998 - Notre Dame Journal of Formal Logic 39 (3):325-331.
    In this paper we define the notion of -linearity for and discuss interpretability (and noninterpretability) of -linear orders in structures and theories.
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  21.  35
    On Reduction Properties.Hirotaka Kikyo & Akito Tsuboi - 1994 - Journal of Symbolic Logic 59 (3):900-911.
  22.  19
    Categoricity and Non-Orthogonality of Types.Akito Tsuboi - 1987 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 33 (4):335-338.
  23.  23
    Definability of Initial Segments.Akito Tsuboi & Saharon Shelah - 2002 - Notre Dame Journal of Formal Logic 43 (2):65-73.
    In any nonstandard model of Peano arithmetic, the standard part is not first-order definable. But we show that in some model the standard part is definable as the unique solution of a formula , where P is a unary predicate variable.
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  24.  6
    Model Companions of Theories of Graphs.Kota Takeuchi, Yu-Ichi Tanaka & Akito Tsuboi - 2015 - Mathematical Logic Quarterly 61 (3):236-246.
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  25.  5
    Amalgamations Preserving ℵ1-Categoricity.Anand Pillay & Akito Tsuboi - 1997 - Journal of Symbolic Logic 62 (4):1070-1074.
  26.  6
    On a Property of Ω-Stable Solvable Groups.Akito Tsuboi - 1988 - Archive for Mathematical Logic 27 (2):193-197.
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  27.  6
    Models Omitting Given Complete Types.Akito Tsuboi - 2008 - Notre Dame Journal of Formal Logic 49 (4):393-399.
    We consider a problem of constructing a model that omits given complete types. We present two results. The first one is related to the Lopez-Escobar theorem and the second one is a version of Morley's omitting types theorem.
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  28.  13
    On Definability of Normal Subgroups of a Superstable Group.Akito Tsuboi - 1992 - Mathematical Logic Quarterly 38 (1):101-106.
    In this note we treat maximal and minimal normal subgroups of a superstable group and prove that these groups are definable under certain conditions. Main tool is a superstable version of Zil'ber's indecomposability theorem.
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  29.  10
    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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  30.  7
    Categoricity and Non‐Orthogonality of Types.Akito Tsuboi - 1987 - Mathematical Logic Quarterly 33 (4):335-338.