Definable Coherent Ultrapowers and Elementary Extensions
Logic
2026-04-30 v4
Abstract
We develop the notion of coherent ultrafilters (extenders without normality or well-foundedness). We then use definable coherent ultraproducts to characterize any extension of a model in any fragment of that defines Skolem functions by a sufficiently complete (but in ) coherent ultrafilter. We apply this method to various elementary classes and AECs.
Keywords
Cite
@article{arxiv.1609.02970,
title = {Definable Coherent Ultrapowers and Elementary Extensions},
author = {Will Boney},
journal= {arXiv preprint arXiv:1609.02970},
year = {2026}
}