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  1. Connected Components of Definable Groups, and o-Minimality II.Annalisa Conversano & Anand Pillay - 2015 - Annals of Pure and Applied Logic 166 (7-8):836-849.
  • On Model-Theoretic Connected Components in Some Group Extensions.Jakub Gismatullin & Krzysztof Krupiński - 2015 - Journal of Mathematical Logic 15 (2):1550009.
  • Smoothness of Bounded Invariant Equivalence Relations.Krzysztof Krupiński & Tomasz Rzepecki - 2016 - Journal of Symbolic Logic 81 (1):326-356.
  • Borel Equivalence Relations and Lascar Strong Types.Krzysztof Krupiński, Anand Pillay & Sławomir Solecki - 2013 - Journal of Mathematical Logic 13 (2):1350008.
  • 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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