Model Completeness for Henselian Fields with finite ramification valued in a $Z$-Group
Logic
2016-03-30 v1
Abstract
We prove that the theory of a Henselian valued field of characteristic zero, with finite ramification, and whose value group is a -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 -adic numbers 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.
Keywords
Cite
@article{arxiv.1603.08598,
title = {Model Completeness for Henselian Fields with finite ramification valued in a $Z$-Group},
author = {Jamshid Derakhshan and Angus Macintyre},
journal= {arXiv preprint arXiv:1603.08598},
year = {2016}
}