Classification Theory and the Construction of PAC Fields
Logic
2026-05-28 v1
Abstract
We analyze a construction of Cherlin, van den Dries, and Macintyre to code graphs in PAC fields. We show that, in many cases, model-theoretic properties of the graph are preserved in the passage from the graph to the field. As a corollary, we show that the SOP hierarchy is strict in the class of fields. The main ingredient is a detailed treatment of the model theory of inverse systems of certain profinite groups that code graphs and can be realized as the absolute Galois groups of PAC fields.
Cite
@article{arxiv.2605.28299,
title = {Classification Theory and the Construction of PAC Fields},
author = {Nicholas Ramsey},
journal= {arXiv preprint arXiv:2605.28299},
year = {2026}
}