# Model Completeness for Henselian Fields with finite ramification valued in a $Z$-Group

Derakhshan, J
Macintyre, A

## Last Updated:

2019-04-17T03:00:56.01+01:00

## 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.

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