2015/09/08 by Immanuel Halupczok, Halupczok, Immanuel, Yimu Yin +1 · 2 citations
Mathematics · #03C64 #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #FOS: Mathematics #Logic (math.LO) #Mathematical Dynamics and Fractals
paper · doi:10.48550/arxiv.1509.02376
openalex publication_date 2015/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.