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Preprint Number 918
918. Immanuel Halupczok and Yimu Yin
Lipschitz stratifications in power-bounded o-minimal fields
Submission date: 8 September 2015.
We propose to grok Lipschitz stratifications from a non-archimedean point of view and thereby show that they exist for closed definable sets, not necessarily compact, 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.
Mathematics Subject Classification: 03C64
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