Hyperdefinable groups in simple theories

Journal of Mathematical Logic 1 (01):125-172 (2001)

We study hyperdefinable groups, the most general kind of groups interpretable in a simple theory. After developing their basic theory, we prove the appropriate versions of Hrushovski's group quotient theorem and the Weil–Hrushovski group chunk theorem. We also study locally modular hyperdefinable groups and prove that they are bounded-by-Abelian-by-bounded. Finally, we analyze hyperdefinable groups in supersimple theories.
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DOI 10.1142/S0219061301000053
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Definability and Definable Groups in Simple Theories.Anand Pillay - 1998 - Journal of Symbolic Logic 63 (3):788-796.

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Constructing an Almost Hyperdefinable Group.Itay Ben-Yaacov, Ivan Tomašić & Frank O. Wagner - 2004 - Journal of Mathematical Logic 4 (02):181-212.
Compactness and Independence in Non First Order Frameworks.Itay Ben-Yaacov - 2005 - Bulletin of Symbolic Logic 11 (1):28-50.
Quelques Réflexions Inévitables.Frank O. Wagner - 2013 - Archive for Mathematical Logic 52 (1-2):159-171.

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