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29 March 2024
 
  » arxiv » 1812.7970

 Article overview


Small sets in Mann pairs
Pantelis E. Eleftheriou ;
Date 19 Dec 2018
AbstractLet $widetilde{mathcal M}=langle mathcal M, G angle$ be an expansion of a real closed field $mathcal M$ by a dense subgroup $G$ of $langle M^{>0}, cdot angle$ with the Mann property. We prove that the induced structure on $G$ by $mathcal M$ eliminates imaginaries. As a consequence, every small set $X$ definable in $mathcal M$ can be definably embedded into some $G^l$, uniformly in parameters. These results are proved in a more general setting, where $widetilde{mathcal M}=langle mathcal M, P angle$ is an expansion of an o-minimal structure $mathcal M$ by a dense set $Psubseteq M$, satisfying three tameness conditions.
Source arXiv, 1812.7970
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