Journal title
arXiv
Last updated
2022-03-07T19:40:13.98+00:00
Abstract
We prove that the theory of a Henselian valued field of characteristic zero, with finite ramification, and whose value group is a $Z$-group, is model-complete in the language of rings if the theory of its residue field is model-complete in the language of rings. We apply this to prove that every infinite algebraic extension of the field of $p$-adic numbers $\Bbb Q_p$ with finite ramification is model-complete in the language of rings. For this, we give a necessary and sufficient condition for model-completeness of the theory of a perfect pseudo-algebraically closed field with pro-cyclic absolute Galois group.
Symplectic ID
614616
Submitted to ORA
On
Publication type
Journal Article
Publication date
29 March 2016