2007/11/01 by Assaf Hasson, Hasson, Assaf, Alf Onshuus +1
Mathematics · #03C45 #03C64 #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #math.LO #msc:03C45 #msc:03C64
paper · pdf · doi:10.48550/arxiv.0711.0122
arxiv created 2007/11/01 · openalex publication_date 2007/11/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give necessary and sufficient geometric conditions for a theory definable in an o-minimal structure to interpret a real closed field. The proof goes through an analysis of thorn-minimal types in super-rosy dependent theories of finite rank. We prove that such theories are coordinatised by thorn-minimal types and that such a type is unstable if an only if every non-algebraic extension thereof is. We conclude that a type is stable if and only if it admits a coordinatisation in thorn-minimal stable types. We also show that non-trivial thorn-minimal stable types extend stable sets.