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Preprint Number 1406

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1406. Nathanaël Mariaule
Model theory of the field of p-adic numbers expanded by a multiplicative subgroup

Submission date: 28 March 2018


Let G be a multiplicative subgroup of ℚ_p. In this paper, we describe the theory of the pair (ℚ_p, G) under the condition that G satisfies Mann property and is small as subset of a first-order structure. First, we give an axiomatisation of the first-order theory of this structure. This includes an axiomatisation of the theory of the group G as valued group (with the valuation induced on G by the p-adic valuation). If the subgroups G^{[n]} of G have finite index for all n, we describe the definable sets in this theory and prove that it is NIP. Finally, we extend some of our results to the subanalytic setting.

Mathematics Subject Classification: 03C65

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Full text arXiv 1803.10564: pdf, ps.

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