Volumes of definable sets in o-minimal expansions and affine GAGA theorems

2021/02/01 by Patrick Brosnan, Brosnan, Patrick
Computer Science · Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.2102.01227

openalex publication_date 2021/02/01 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

In this mostly expository note, I give a very quick proof of the definable Chow theorem of Peterzil and Starchenko using the Bishop-Stoll theorem and a volume estimate for definable sets due to Nguyen and Valette. The volume estimate says that any d-dimensional definable subset of S⊆ℝⁿ in an o-minimal expansion of the ordered field of real numbers satisfies the inequality H^d(\x∈ S:‖ x‖

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