Two examples concerning existential undecidability in fields
Logic
2025-07-16 v1
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.
Keywords
Cite
@article{arxiv.2211.01775,
title = {Two examples concerning existential undecidability in fields},
author = {Philip Dittmann},
journal= {arXiv preprint arXiv:2211.01775},
year = {2025}
}