Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 2031

Preprint Number 2031

Previous Next Preprint server

2031. Victor Lisinski
Decidability of positive characteristic tame Hahn fields in L_t

Submission date: 9 August 2021


We show that any positive characteristic tame Hahn field 𝔽((t^Γ)) containing t is decidable in L_t, the language of valued fields with a constant symbol for t, if 𝔽 and Γ are decidable. In particular, we obtain decidability of 𝔽_p((t^{1/p^{∞}})) and 𝔽_p((t^ℚ)) in L_t. This uses a new AKE-principle for equal characteristic tame fields in L_t, building on work by Kuhlmann, together with Kedlaya's work on finite automata and algebraic extensions of function fields. In the process, we obtain an AKE-principle for tame fields in mixed characteristic and recover a theorem by Rayner on the relative algebraic closure of function fields inside Hahn fields.

Mathematics Subject Classification:

Keywords and phrases:

Full text arXiv 2108.04132: pdf, ps.

Last updated: August 23 2021 16:50 Please send your corrections to: