Hausdorff limits of Rolle leaves
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas - Tập 107 - Trang 79-89 - 2012
Tóm tắt
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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