Two examples concerning existential undecidability in fields

2022/11/03 by Philip Dittmann, Dittmann, Philip
Mathematics · #03C60 #12L05 #Advanced Topology and Set Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.2211.01775

openalex publication_date 2022/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct an existentially undecidable complete discretely valued field of mixed characteristic with existentially decidable residue field and decidable algebraic part, answering a question by Anscombe-Fehm in a strong way. Along the way, we construct an existentially decidable field of positive characteristic with an existentially undecidable finite extension, modifying a construction due to Kesavan Thanagopal.

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