2024/03/26 by Will Johnson, Johnson, Will · 1 citation
Mathematics · #03C60 #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #Mathematical Dynamics and Fractals #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2403.17478
openalex publication_date 2024/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that C-minimal fields (i.e., C-minimal expansions of ACVF) have the exchange property, answering a question of Haskell and Macpherson. Additionally, we strengthen some theorems of Cubides Kovacsics and Delon on C-minimal fields. First, we show that definably complete C-minimal fields of characteristic 0 have generic differentiability. Second, we show that if the induced structure on the residue field is a pure ACF, then polynomial boundedness holds. In fact, polynomial boundedness can only fail if there are unexpected definable automorphisms of the multiplicative group of the residue field.