O-minimal residue fields of o-minimal fields

2010/01/11 by Jana Maříková, Maříková, Jana
Mathematics · #03C64 #Advanced Topology and Set Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1001.1575

openalex publication_date 2010/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R be an o-minimal field with a proper convex subring V. We axiomatize the class of all structures (R,V) such that k_ind, the corresponding residue field with structure induced from R via the residue map, is o-minimal. More precisely, in previous work it was shown that certain first order conditions on (R,V) are sufficient for the o-minimality of k_ind. Here we prove that these conditions are also necessary.

Citations

• PL and differential topology in o-minimal structure

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