29 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.  2
    Random structures and automorphisms with a single orbit.Hirotaka Kikyo & Akito Tsuboi - forthcoming - Archive for Mathematical Logic:1-11.
    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 $$m \ge 3$$ m ≥ 3, we demonstrate that the random structure for the class has continuum-many automorphisms with a single orbit. (...)
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  3.  24
    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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  4.  34
    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.  18
    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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  6.  33
    Algebraic types and automorphism groups.Akito Tsuboi - 1993 - Journal of Symbolic Logic 58 (1):232-239.
  7.  33
    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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  8.  17
    A construction of real closed fields.Yu-Ichi Tanaka & Akito Tsuboi - 2015 - Mathematical Logic Quarterly 61 (3):159-168.
    We introduce a new construction of real closed fields by using an elementary extension of an ordered field with an integer part satisfying. This method can be extend to a finite extension of an ordered field with an integer part satisfying. In general, a field obtained from our construction is either real closed or algebraically closed, so an analogy of Ostrowski's dichotomy holds. Moreover we investigate recursive saturation of an o‐minimal extension of a real closed field by finitely many function (...)
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  9.  24
    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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  10.  70
    On reduction properties.Hirotaka Kikyo & Akito Tsuboi - 1994 - Journal of Symbolic Logic 59 (3):900-911.
  11.  26
    (1 other version)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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  12. On the number of independent partitions.Akito Tsuboi - 1985 - Journal of Symbolic Logic 50 (3):809-814.
  13.  95
    On theories having a finite number of nonisomorphic countable models.Akito Tsuboi - 1985 - Journal of Symbolic Logic 50 (3):806-808.
  14.  52
    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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  15.  42
    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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  16.  23
    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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  17.  9
    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 - World Scientific Publishing Company.
    The Asian Logic Conference (ALC) is a major international event in mathematical logic. It features the latest scientific developments in the fields of mathematical logic and its applications, logic in computer science, and philosophical logic. The ALC series also aims to promote mathematical logic in the Asia-Pacific region and to bring logicians together both from within Asia and elsewhere for an exchange of information and ideas. This combined proceedings volume represents works presented or arising from the 14th and 15th ALCs.
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  18.  81
    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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  19.  2
    Dividing and forking in random hypergraphs.Hirotaka Kikyo & Akito Tsuboi - 2025 - Annals of Pure and Applied Logic 176 (2):103521.
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  20.  19
    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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  21.  31
    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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  22.  23
    Model companions of theories of graphs.Kota Takeuchi, Yu-Ichi Tanaka & Akito Tsuboi - 2015 - Mathematical Logic Quarterly 61 (3):236-246.
    We study model companions of theories extending the graph axioms. First we prove general results concerning the existence of the model companion. Then, by applying these results to the case of graphs, we give a series of companionable and non‐companionable examples.
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  23.  18
    On the number of independent orders.Kota Takeuchi & Akito Tsuboi - 2021 - Annals of Pure and Applied Logic 172 (2):102886.
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  24.  21
    (1 other version)Categoricity and Non‐Orthogonality of Types.Akito Tsuboi - 1987 - Mathematical Logic Quarterly 33 (4):335-338.
  25.  23
    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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  26.  22
    Nonstandard methods for finite structures.Akito Tsuboi - 2020 - Mathematical Logic Quarterly 66 (3):367-372.
    We discuss the possibility of applying the compactness theorem to the study of finite structures. Given a class of finite structures, it is important to determine whether it can be expressed by a particular category of sentences. We are interested in this type of problem, and use nonstandard method for showing the non‐expressibility of certain classes of finite graphs by an existential monadic second order sentence.
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  27.  21
    On a property of ω-stable solvable groups.Akito Tsuboi - 1988 - Archive for Mathematical Logic 27 (2):193-197.
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  28.  30
    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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  29.  47
    Strongly 2-dimensional theories.Akito Tsuboi - 1988 - Journal of Symbolic Logic 53 (3):931-936.