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  1.  11
    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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  2.  10
    Elementary equivalence theorem for Pac structures.Jan Dobrowolski, Daniel Max Hoffmann & Junguk Lee - 2020 - Journal of Symbolic Logic 85 (4):1467-1498.
    We generalize a well-known theorem binding the elementary equivalence relation on the level of PAC fields and the isomorphism type of their absolute Galois groups. Our results concern two cases: saturated PAC structures and nonsaturated PAC structures.
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  3.  5
    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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  4.  15
    On Rank Not Only in Nsop Theories.Jan Dobrowolski & Daniel Max Hoffmann - forthcoming - Journal of Symbolic Logic:1-34.
    We introduce a family of local ranks $D_Q$ depending on a finite set Q of pairs of the form $(\varphi (x,y),q(y)),$ where $\varphi (x,y)$ is a formula and $q(y)$ is a global type. We prove that in any NSOP $_1$ theory these ranks satisfy some desirable properties; in particular, $D_Q(x=x)<\omega $ for any finite tuple of variables x and any Q, if $q\supseteq p$ is a Kim-forking extension of types, then $D_Q(q) (...)
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  5.  7
    A preservation theorem for theories without the tree property of the first kind.Jan Dobrowolski & Hyeungjoon Kim - 2017 - Mathematical Logic Quarterly 63 (6):536-543.
    We prove the NTP1 property of a geometric theory T is inherited by theories of lovely pairs and H‐structures associated to T. We also provide a class of examples of nonsimple geometric NTP1 theories.
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  6.  1
    Generic variations and NTP$$_1$$1.Jan Dobrowolski - 2018 - Archive for Mathematical Logic 57 (7-8):861-871.
    We prove a preservation theorem for NTP\ in the context of the generic variations construction. We also prove that NTP\ is preserved under adding to a geometric theory a generic predicate.
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  7.  5
    On ω-categorical, generically stable groups.Jan Dobrowolski & Krzysztof Krupiński - 2012 - Journal of Symbolic Logic 77 (3):1047-1056.
    We prove that each ω-categorical, generically stable group is solvable-by-finite.
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  8.  3
    New examples of small Polish structures.Jan Dobrowolski - 2013 - Journal of Symbolic Logic 78 (3):969-976.
  9.  9
    On ω-categorical, generically stable groups and rings.Jan Dobrowolski & Krzysztof Krupiński - 2013 - Annals of Pure and Applied Logic 164 (7-8):802-812.
    We prove that every ω-categorical, generically stable group is nilpotent-by-finite and that every ω-categorical, generically stable ring is nilpotent-by-finite.
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  10.  3
    Some remarks on inp-minimal and finite burden groups.Jan Dobrowolski & John Goodrick - 2019 - Archive for Mathematical Logic 58 (3-4):267-274.
    We prove that any left-ordered inp-minimal group is abelian and we provide an example of a non-abelian left-ordered group of dp-rank 2. Furthermore, we establish a necessary condition for a group to have finite burden involving normalizers of definable sets, reminiscent of other chain conditions for stable groups.
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  11.  5
    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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