Submission date: 29 March 2016.

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 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.

Mathematics Subject Classification: 03C10, 03C60, 03C65, 12E30, 12J20, 12J25, 12J12, 11U09

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Full text arXiv 1603.08598: pdf, ps.