Sheaves of structures, Heyting‐valued structures, and a generalization of Łoś's theorem. Issue 4 (20th November 2021)

• Record Type: Journal Article
• Authors: Aratake, Hisashi
• Is Part Of: Mathematical logic quarterly. Volume 67:Issue 4(2021)
• Page Start: 445
• Page End: 468
• Publication Date: 2021-11-20
• Subjects: Mathematics -- Periodicals; Logic, Symbolic and mathematical -- Periodicals; 511.3
• DOI: 10.1002/malq.202000088
• Languages: English
• ISSNs: 0942-5616

Abstract

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.