Ultrafilter extensions of bounded graphs are elementary
Logic
2024-05-28 v1
Abstract
The main motivation of this paper is the study of first-order model theoretic properties of structures having their roots in modal logic. We will focus on the connections between ultrafilter extensions and ultrapowers. We show that certain structures (called bounded graphs) are elementary substructures of their ultrafilter extensions, moreover their modal logics coincide.
Keywords
Cite
@article{arxiv.2405.17101,
title = {Ultrafilter extensions of bounded graphs are elementary},
author = {Zalán Molnár},
journal= {arXiv preprint arXiv:2405.17101},
year = {2024}
}