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March 2010 Fields interpretable in superrosy groups with NIP (the non-solvable case)
Krzysztof Krupiński
J. Symbolic Logic 75(1): 372-386 (March 2010). DOI: 10.2178/jsl/1264433927

Abstract

Let G be a group definable in a monster model 𝔠 of a rosy theory satisfying NIP. Assume that G has hereditarily finitely satisfiable generics and 1 < Uþ(G) < ∞. We prove that if G acts definably on a definable set of Uþ-rank 1, then, under some general assumption about this action, there is an infinite field interpretable in 𝔠. We conclude that if G is not solvable-by-finite and it acts faithfully and definably on a definable set of Uþ-rank 1, then there is an infinite field interpretable in 𝔠. As an immediate consequence, we get that if G has a definable subgroup H such that Uþ(G)=Uþ(H)+1 and G/⋂g ∈ GHg is not solvable-by-finite, then an infinite field interpretable in 𝔠 also exists.

Citation

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Krzysztof Krupiński. "Fields interpretable in superrosy groups with NIP (the non-solvable case)." J. Symbolic Logic 75 (1) 372 - 386, March 2010. https://doi.org/10.2178/jsl/1264433927

Information

Published: March 2010
First available in Project Euclid: 25 January 2010

zbMATH: 1195.03039
MathSciNet: MR2605900
Digital Object Identifier: 10.2178/jsl/1264433927

Subjects:
Primary: 03C45, 03C60

Rights: Copyright © 2010 Association for Symbolic Logic

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Vol.75 • No. 1 • March 2010
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