A topos for continuous logic
Logic
2021-07-23 v1 Category Theory
Abstract
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.
Cite
@article{arxiv.2107.10543,
title = {A topos for continuous logic},
author = {Daniel Figueroa and Benno van den Berg},
journal= {arXiv preprint arXiv:2107.10543},
year = {2021}
}