Finite burden in multivalued algebraically closed fields

2019/05/13 by Will Johnson, Johnson, Will
Mathematics · #03C10 #03C45 #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Logic (math.LO) #Rings, Modules, and Algebras #math.LO #msc:03C10 #msc:03C45

paper · pdf · doi:10.48550/arxiv.1905.04991

40 pages

arxiv created 2019/05/13 · openalex publication_date 2019/05/13 · arxiv updated 2019/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that an expansion of an algebraically closed field by n arbitrary valuation rings is NTP₂, and in fact has finite burden. It fails to be NIP, however, unless the valuation rings form a chain. Moreover, the incomplete theory of algebraically closed fields with n valuation rings is decidable.

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