Mathematics > Logic
arXiv:2605.28299 (math)
[Submitted on 27 May 2026]
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$_{n}$ 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.
Submission history
From: Nicholas Ramsey [view email]
[v1]
Wed, 27 May 2026 10:49:46 UTC (72 KB)
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