Lipschitz stratifications in power-bounded o-minimal fields
Abstract
We propose to grok Lipschitz stratifications from a non-archimedean point of view and thereby show that they exist for closed definable sets in any power-bounded o-minimal structure on a real closed field. Unlike the previous approaches in the literature, our method bypasses resolution of singularities and Weierstrass preparation altogether; it transfers the situation to a non-archimedean model, where the quantitative estimates appearing in Lipschitz stratifications are sharpened into valuation-theoretic inequalities. Applied to a uniform family of sets, this approach automatically yields a family of stratifications which satisfy the Lipschitz conditions in a uniform way.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2015
- DOI:
- 10.48550/arXiv.1509.02376
- arXiv:
- arXiv:1509.02376
- Bibcode:
- 2015arXiv150902376H
- Keywords:
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- Mathematics - Logic;
- Mathematics - Algebraic Geometry;
- 03C64
- E-Print:
- 44 pages, 5 figures