## Works by Byunghan Kim

26 found
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1. Simple Theories.Byunghan Kim & Anand Pillay - 1996 - Annals of Pure and Applied Logic 88 (2):149-164.

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2. Notions Around Tree Property 1.Byunghan Kim & Hyeung-Joon Kim - 2011 - Annals of Pure and Applied Logic 162 (9):698-709.
In this paper, we study the notions related to tree property 1 , or, equivalently, SOP2. Among others, we supply a type-counting criterion for TP1 and show the equivalence of TP1 and k- TP1. Then we introduce the notions of weak k- TP1 for k≥2, and also supply type-counting criteria for those. We do not know whether weak k- TP1 implies TP1, but at least we prove that each weak k- TP1 implies SOP1. Our generalization of the tree-indiscernibility results in (...)

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3. Tree Indiscernibilities, Revisited.Byunghan Kim, Hyeung-Joon Kim & Lynn Scow - 2014 - Archive for Mathematical Logic 53 (1-2):211-232.
We give definitions that distinguish between two notions of indiscernibility for a set {aη∣η∈ω>ω}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\{a_{\eta} \mid \eta \in ^{\omega>}\omega\}}$$\end{document} that saw original use in Shelah [Classification theory and the number of non-isomorphic models. North-Holland, Amsterdam, 1990], which we name s- and str−indiscernibility. Using these definitions and detailed proofs, we prove s- and str-modeling theorems and give applications of these theorems. In particular, we verify a step in the argument that TP is equivalent (...)
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4. Simplicity, and Stability in There.Byunghan Kim - 2001 - Journal of Symbolic Logic 66 (2):822-836.
Firstly, in this paper, we prove that the equivalence of simplicity and the symmetry of forking. Secondly, we attempt to recover definability part of stability theory to simplicity theory. In particular, using elimination of hyperimaginaries we prove that for any supersimple T, canonical base of an amalgamation class P is the union of names of ψ-definitions of P, ψ ranging over stationary L-formulas in P. Also, we prove that the same is true with stable formulas for an 1-based theory having (...)

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5. Constructing the Hyperdefinable Group From the Group Configuration.Tristram de Piro, Byunghan Kim & Jessica Millar - 2006 - Journal of Mathematical Logic 6 (2):121-139.
Under [Formula: see text]-amalgamation, we obtain the canonical hyperdefinable group from the group configuration.

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6. The Lascar Groups and the First Homology Groups in Model Theory.Jan Dobrowolski, Byunghan Kim & Junguk Lee - 2017 - Annals of Pure and Applied Logic 168 (12):2129-2151.

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7. Type-Amalgamation Properties and Polygroupoids in Stable Theories.John Goodrick, Byunghan Kim & Alexei Kolesnikov - 2015 - Journal of Mathematical Logic 15 (1):1550004.
We show that in a stable first-order theory, the failure of higher dimensional type amalgamation can always be witnessed by algebraic structures that we call n-ary polygroupoids. This generalizes a result of Hrushovski in [16] that failures of 4-amalgamation are witnessed by definable groupoids. The n-ary polygroupoids are definable in a mild expansion of the language.

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8. Homology Groups of Types in Model Theory and the Computation of H 2.John Goodrick, Byunghan Kim & Alexei Kolesnikov - 2013 - Journal of Symbolic Logic 78 (4):1086-1114.

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9. From Stability to Simplicity.Byunghan Kim & Anand Pillay - 1998 - Bulletin of Symbolic Logic 4 (1):17-36.
§1. Introduction. In this report we wish to describe recent work on a class of first order theories first introduced by Shelah in [32], the simple theories. Major progress was made in the first author's doctoral thesis [17]. We will give a survey of this, as well as further works by the authors and others.The class of simple theories includes stable theories, but also many more, such as the theory of the random graph. Moreover, many of the theories of particular (...)

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10. A Note on Lascar Strong Types in Simple Theories.Byunghan Kim - 1998 - Journal of Symbolic Logic 63 (3):926-936.
Let T be a countable, small simple theory. In this paper, we prove that for such T, the notion of Lascar strong type coincides with the notion of strong type, over an arbitrary set.

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11. 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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12. Homology Groups of Types in Model Theory and the Computation of $H_2$.John Goodrick, Byunghan Kim & Alexei Kolesnikov - 2013 - Journal of Symbolic Logic 78 (4):1086-1114.

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13. A Supersimple Nonlow Theory.Enrique Casanovas & Byunghan Kim - 1998 - Notre Dame Journal of Formal Logic 39 (4):507-518.
This paper presents an example of a supersimple nonlow theory and characterizes its independence relation.

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14. Homology Groups of Types in Stable Theories and the Hurewicz Correspondence.John Goodrick, Byunghan Kim & Alexei Kolesnikov - 2017 - Annals of Pure and Applied Logic 168 (9):1710-1728.

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15. Simplicity Theory.Byunghan Kim - 2013 - Oxford University Press.
An up-to-date account of the current techniques and results in Simplicity Theory, which has been a focus of research in model theory for the last decade. Suitable for logicians, mathematicians and graduate students working on model theory.

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16. A Classification of 2-Chains Having 1-Shell Boundaries in Rosy Theories.Byunghan Kim, Sunyoung Kim & Junguk Lee - 2015 - Journal of Symbolic Logic 80 (1):322-340.

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17. A Note on Weak Dividing.Byunghan Kim & Niandong Shi - 2007 - Archive for Mathematical Logic 46 (2):51-60.
We study the notion of weak dividing introduced by S. Shelah. In particular we prove that T is stable iff weak dividing is symmetric.

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19. Stable Definability and Generic Relations.Byunghan Kim & Rahim Moosa - 2007 - Journal of Symbolic Logic 72 (4):1163 - 1176.
An amalgamation base p in a simple theory is stably definable if its canonical base is interdefinable with the set of canonical parameters for the ϕ-definitions of p as ϕ ranges through all stable formulae. A necessary condition for stably definability is given and used to produce an example of a supersimple theory with stable forking having types that are not stably definable. This answers negatively a question posed in [8]. A criterion for and example of a stably definable amalgamation (...)

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20. Recovering the Hyperdefinable Group Action in the Group Configuration Theorem.Byunghan Kim - 2010 - Journal of Symbolic Logic 75 (1):12-24.
In this paper, we continue the construction done in [3], so that under model-4-CA or 4-CA, given a bounded quadrangle C induced from a group configuration, we build a canonical hyperdefinable homogeneous space equivalent to C. When C is principal, we can choose the homogeneous space principal as well.

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21. With Student Day on December 14, 2011.Sergei S. Goncharov, Byunghan Kim & Greg Restall - 2013 - Bulletin of Symbolic Logic 19 (2).

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22. On the Number of Countable Models of a Countable Nsop1 Theory Without Weight Ω.Byunghan Kim - 2019 - Journal of Symbolic Logic 84 (3):1168-1175.
In this article, we prove that if a countable non-${\aleph _0}$-categorical NSOP1 theory with nonforking existence has finitely many countable models, then there is a finite tuple whose own preweight is ω. This result is an extension of a theorem of the author on any supersimple theory.

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23. Independence Over Arbitrary Sets in NSOP1 Theories.Jan Dobrowolski, Byunghan Kim & Nicholas Ramsey - 2022 - Annals of Pure and Applied Logic 173 (2):103058.
We study Kim-independence over arbitrary sets. Assuming that forking satisfies existence, we establish Kim's lemma for Kim-dividing over arbitrary sets in an NSOP1 theory. We deduce symmetry of Kim-independence and the independence theorem for Lascar strong types.
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24. The Relativized Lascar Groups, Type-Amalgamation, and Algebraicity.Jan Dobrowolski, Byunghan Kim, Alexei Kolesnikov & Junguk Lee - 2021 - Journal of Symbolic Logic 86 (2):531-557.
In this paper we study the relativized Lascar Galois group of a strong type. The group is a quasi-compact connected topological group, and if in addition the underlying theory T is G-compact, then the group is compact. We apply compact group theory to obtain model theoretic results in this note. -/- For example, we use the divisibility of the Lascar group of a strong type to show that, in a simple theory, such types have a certain model theoretic property that (...)

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25. The Lascar Group and the Strong Types of Hyperimaginaries.Byunghan Kim - 2013 - Notre Dame Journal of Formal Logic 54 (3-4):497-507.
This is an expository note on the Lascar group. We also study the Lascar group over hyperimaginaries and make some new observations on the strong types over those. In particular, we show that in a simple theory $\operatorname{Ltp}\equiv\operatorname{stp}$ in real context implies that for hyperimaginary context.
We study the notion of weak canonical bases in an NSOP $_{1}$ theory T with existence. Given $p=\operatorname {tp}$ where $B=\operatorname {acl}$ in ${\mathcal M}^{\operatorname {eq}}\models T^{\operatorname {eq}}$, the weak canonical base of p is the smallest algebraically closed subset of B over which p does not Kim-fork. With this aim we firstly show that the transitive closure $\approx$ of collinearity of an indiscernible sequence is type-definable. Secondly, we prove that given a total \$\mathop {\smile \hskip -0.9em ^| \ (...)