Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Model Completeness for Henselian Fields with finite ramification valued
  in a $Z$-Group   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.

17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex