# Model theory of finite-by-Presburger Abelian groups and finite extensions of $p$-adic fields

Derakhshan, J
Macintyre, A

## Last Updated:

2019-04-17T03:00:56.15+01:00

## 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).

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