Sheaves of Structures, Heyting-Valued Structures, and a Generalization of Łoś's Theorem
arXiv:2012.04317 · doi:10.1002/malq.202000088
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 Łoś's theorem for Heyting-valued structures. We also give a characterization of Heyting-valued structures for which Łoś's theorem holds with respect to any maximal filter.
arXiv comment34 pages