A topos for continuous logic

Daniel Figueroa and Benno van den Berg

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.

Keywords: Continuous logic, metric spaces, categorical logic, hyperdoctrines, Grothendieck toposes

2020 MSC: 03C66,03G30,18F10

Theory and Applications of Categories, Vol. 38, 2022, No. 28, pp 1108-1135.

Published 2022-09-07.


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