publication . Preprint . 2017

Definably compact groups definable in real closed fields.II

Barriga, Eliana;
Open Access English
  • Published: 20 May 2017
Abstract
We continue the analysis of definably compact groups definable in a real closed field $\mathcal{R}$. In [3], we proved that for every definably compact definably connected semialgebraic group $G$ over $\mathcal{R}$ there are a connected $R$-algebraic group $H$, a definable injective map $\phi$ from a generic definable neighborhood of the identity of $G$ into the group $H\left(R\right)$ of $R$-points of $H$ such that $\phi$ acts as a group homomorphism inside its domain. The above result and our study of locally definable covering homomorphisms for locally definable groups combine to prove that if such group $G$ is in addition abelian, then its o-minimal universa...
Subjects
free text keywords: Mathematics - Logic, 03C64, 20G20, 22E15, 03C68, 22B99
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