4 found
  1.  13
    On Compactifications and the Topological Dynamics of Definable Groups.Jakub Gismatullin, Davide Penazzi & Anand Pillay - 2014 - Annals of Pure and Applied Logic 165 (2):552-562.
    For G a group definable in some structure M, we define notions of “definable” compactification of G and “definable” action of G on a compact space X , where the latter is under a definability of types assumption on M. We describe the universal definable compactification of G as View the MathML source and the universal definable G-ambit as the type space SG. We also point out the existence and uniqueness of “universal minimal definable G-flows”, and discuss issues of amenability (...)
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  2.  61
    G-Compactness and Groups.Jakub Gismatullin & Ludomir Newelski - 2008 - Archive for Mathematical Logic 47 (5):479-501.
    Lascar described E KP as a composition of E L and the topological closure of E L (Casanovas et al. in J Math Log 1(2):305–319). We generalize this result to some other pairs of equivalence relations. Motivated by an attempt to construct a new example of a non-G-compact theory, we consider the following example. Assume G is a group definable in a structure M. We define a structure M′ consisting of M and X as two sorts, where X is an (...)
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  3.  10
    Model Theoretic Connected Components of Finitely Generated Nilpotent Groups.Nathan Bowler, Cong Chen & Jakub Gismatullin - 2013 - Journal of Symbolic Logic 78 (1):245-259.
    We prove that for a finitely generated infinite nilpotent group $G$ with structure $(G,\cdot,\dots)$, the connected component ${G^*}^0$ of a sufficiently saturated extension $G^*$ of $G$ exists and equals \[ \bigcap_{n\in\N} \{g^n\colon g\in G^*\}. \] We construct an expansion of ${\mathbb Z}$ by a predicate $({\mathbb Z},+,P)$ such that the type-connected component ${{\mathbb Z}^*}^{00}_{\emptyset}$ is strictly smaller than ${{\mathbb Z}^*}^0$. We generalize this to finitely generated virtually solvable groups. As a corollary of our construction we obtain an optimality result for (...)
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  4.  11
    On Model-Theoretic Connected Components in Some Group Extensions.Jakub Gismatullin & Krzysztof Krupiński - 2015 - Journal of Mathematical Logic 15 (2):1550009.