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Small sets in dense pairs | | Pantelis E. Eleftheriou
; | | Date: |
19 Apr 2017 | | Abstract: | Let $widetilde{mathcal M}=langle mathcal M, P
angle$ be an expansion of
an o-minimal structure $mathcal M$ by a dense set $Psubseteq M$, such that
three tameness conditions hold. We prove that the induced structure on $P$ by
$mathcal M$ eliminates imaginaries. As a corollary, we obtain that every small
set $X$ definable in $widetilde{mathcal M}$ can be definably embedded into
some $P^l$, uniformly in parameters. We verify the tameness conditions in three
examples: dense pairs, expansions of $mathcal M$ by a dense independent set,
and expansions by a dense divisible multiplicative group with the Mann
property. | | Source: | arXiv, 1704.5802 | | Services: | Forum | Review | PDF | Favorites | |
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