Reflection Into Models of Finite Decidable FP-sketches in an Arithmetic Universe

Authors:
Maria Emilia Maietti
Affiliations:
Dipartimento di Matematica Pura ed Applicata, University of Padova, via Belzoni n.7, 35100 Padova, Italy
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2005

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Abstract

We consider finite decidable FP-sketches within an arithmetic universe. By an FP-sketch we mean a sketch with terminal and binary product cones. By an arithmetic universe we mean a list-arithmetic pretopos, which is the general categorical definition we give to the concept of arithmetic universe introduced by Andre Joyal to prove Godel incompleteness theorems. Then, for finite decidable FP-sketches we prove a constructive version of Ehresmann-Kennison's theorem stating that the category of models of finite decidable FP-sketches in an arithmetic universe is reflective in the corresponding category of graph morphisms. The proof is done by employing the internal dependent type theory of an arithmetic universe.