English

A P-adic structure which does not interpret an infinite field but whose Shelah completion does

Logic 2020-06-02 v1

Abstract

We give a pp-adic example of a structure whose Shelah completion interprets Qp\mathbb{Q}_p but which does not (provided an extremely plausible conjecture holds) interpret an infinite field. In the final section we discuss the significance of such examples for a possible future geometric theory of NIP\mathrm{NIP} structures.

Cite

@article{arxiv.2006.00137,
  title  = {A P-adic structure which does not interpret an infinite field but whose Shelah completion does},
  author = {Erik Walsberg},
  journal= {arXiv preprint arXiv:2006.00137},
  year   = {2020}
}
R2 v1 2026-06-23T15:55:25.216Z