SeminĂ¡rios de Teoria dos Modelos

18 de Março 2009, 14h00

Torsion-freeness of G00 in the abelian case
Complexo Interdisciplinar, Sala B3-01

A. USVYATSOV (CMAF - Universidade de Lisboa)

Abstract:

We will prove the following theorem: Let G be a definably compact definably connected abelian group definable in an o-minimal expansion of a field. Then G^{00} is torsion free. The proof splits into two parts: 1. For every definable set X, Stab(X) is a type-definable subgroup of G. This uses some general nonsense about generic sets. 2. Stab(X) is of bounded index in G. This uses dependence and Keisler measures.

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