Imaginaries and invariant types in existentially closed valued\n differential fields

2015/08/31 by Silvain Rideau-Kikuchi, Rideau, Silvain
Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.1508.07935

openalex publication_date 2015/08/31 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We answer two open questions about the model theory of valued differential\nfields introduced by Scanlon. We show that they eliminate imaginaries in the\ngeometric language introduced by Haskell, Hrushovski and Macpherson and that\nthey have the invariant extension property. These two result follow from an\nabstract criterion for the density of definable types in enrichments of\nalgebraically closed valued fields. Finally, we show that this theory is\nmetastable.\n

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