Corpus ID: 73662780

# Model theory of the field of \$p\$-adic numbers expanded by a multiplicative subgroup

```@article{Mariaule2018ModelTO,
title={Model theory of the field of \\$p\\$-adic numbers expanded by a multiplicative subgroup},
author={Nathanael Mariaule},
journal={arXiv: Logic},
year={2018}
}```
Let \$G\$ be a multiplicative subgroup of \$\mathbb{Q}_p\$. In this paper, we describe the theory of the pair \$(\mathbb{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… Expand

#### References

SHOWING 1-10 OF 24 REFERENCES
THE FIELD OF p-ADIC NUMBERS WITH A PREDICATE FOR THE POWERS OF AN INTEGER
A Version of o-Minimality for the p-adics
• Mathematics, Computer Science
• J. Symb. Log.
• 1997
Presburger sets and p-minimal fields
• R. Cluckers
• Mathematics, Computer Science
• Journal of Symbolic Logic
• 2003
Solution of a Problem of Tarski
• J. Myhill
• Mathematics, Computer Science
• J. Symb. Log.
• 1956