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Small sets in Mann pairs | Pantelis E. Eleftheriou
; | Date: |
19 Dec 2018 | Abstract: | Let $widetilde{mathcal M}=langle mathcal M, G
angle$ 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 | Services: | Forum | Review | PDF | Favorites |
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