2021/07/22 by Daniel G. Figueroa, Figueroa, Daniel, Benno van den Berg +1
Computer Science · #Advanced Algebra and Logic #Category Theory (math.CT) #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems
paper · pdf · doi:10.48550/arxiv.2107.10543
openalex publication_date 2021/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We suggest an ordering for the predicates in continuous logic so that the semantics of continuous logic can be formulated as a hyperdoctrine. We show that this hyperdoctrine can be embedded into the hyperdoctrine of subobjects of a suitable Grothendieck topos. For this embedding we use a simplification of the hyperdoctrine for continuous logic, whose category of equivalence relations is equivalent to the category of complete metric spaces and uniformly continuous maps.