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

Jamshid Derakhshan; Angus Macintyre

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arXiv · 1603.08601

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

Jamshid Derakhshan·Angus Macintyre

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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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BibTeX RIS

Jamshid Derakhshan, Angus Macintyre. 2016-03-29. Model theory of finite-by-Presburger Abelian groups and finite extensions of $p$-adic fields. https://arxiv.org/abs/1603.08601

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