Ultrafilter extensions of bounded graphs are elementary

Zalán Molnár

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arXiv · 2405.17101

Ultrafilter extensions of bounded graphs are elementary

Zalán Molnár

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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.

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BibTeX RIS

Zalán Molnár. 2024-05-27. Ultrafilter extensions of bounded graphs are elementary. https://arxiv.org/abs/2405.17101

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