Sheaves of Structures, Heyting-Valued Structures, and a Generalization of {\L}o\'s's Theorem
Logic
2021-12-15 v1 Category Theory
Abstract
Sheaves of structures are useful to give constructions in universal algebra and model theory. We can describe their logical behavior in terms of Heyting-valued structures. In this paper, we first provide a systematic treatment of sheaves of structures and Heyting-valued structures from the viewpoint of categorical logic. We then prove a form of {\L}o\'s's theorem for Heyting-valued structures. We also give a characterization of Heyting-valued structures for which {\L}o\'s's theorem holds with respect to any maximal filter.
Keywords
Cite
@article{arxiv.2012.04317,
title = {Sheaves of Structures, Heyting-Valued Structures, and a Generalization of {\L}o\'s's Theorem},
author = {Hisashi Aratake},
journal= {arXiv preprint arXiv:2012.04317},
year = {2021}
}
Comments
34 pages