Submission date: 3 November 2022

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.

Mathematics Subject Classification: 12L05, 03C60

Keywords and phrases:

Full text arXiv 2211.01775: pdf, ps).