Submission date: 29 March 2016.

Abstract:

We define a class of pre-ordered abelian groups that we call finite-by-Presburger groups, and prove that their theory is model-complete. We show that certain quotients of the multiplicative group of a local field of characteristic zero are finite-by-Presburger and interpret the higher residue rings of the local field. We apply these results to give a new proof of the model completeness in the ring language of a local field of characteristic zero (a result that follows also from work of Prestel-Roquette).

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

Keywords and phrases:

Full text arXiv 1603.08601: pdf, ps.