Abstract
Let \({\mathcal{R}}\) be an o-minimal expansion of the real field. We introduce a class of Hausdorff limits, the T ∞-limits over \({\mathcal{R}}\), that do not in general fall under the scope of Marker and Steinhorn’s definability-of-types theorem. We prove that if \({\mathcal{R}}\) admits analytic cell decomposition, then every T ∞-limit over \({\mathcal{R}}\) is definable in the pfaffian closure of \({\mathcal{R}}\).
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To Professor Heisuke Hironaka on the occasion of his 80th birthday
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Lion, JM., Speissegger, P. Hausdorff limits of Rolle leaves. RACSAM 107, 79–89 (2013). https://doi.org/10.1007/s13398-012-0089-z
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DOI: https://doi.org/10.1007/s13398-012-0089-z