Two examples concerning existential undecidability in fields

Philip Dittmann

doi:10.1017/jsl.2023.87

Two examples concerning existential undecidability in fields

Philip Dittmann

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Journal	The Journal of Symbolic Logic
DOIs	https://doi.org/10.1017/jsl.2023.87
Publication status	Published - 23 Nov 2023

Keywords

undecidable
existential theory
complete discretely valued field

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10.1017/jsl.2023.87Licence: CC BY

Cite this

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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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Two examples concerning existential undecidability in fields

Abstract

Keywords

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