Sheaves of Structures, Heyting-Valued Structures, and a Generalization of Łoś's Theorem

Hisashi Aratake

doi:10.1002/malq.202000088

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arXiv · 2012.04317

Sheaves of Structures, Heyting-Valued Structures, and a Generalization of Łoś's Theorem

Hisashi Aratake

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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.

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BibTeX RIS

Hisashi Aratake. 2020-12-08. Sheaves of Structures, Heyting-Valued Structures, and a Generalization of Łoś's Theorem. https://doi.org/10.1002/malq.202000088

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