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math.LO2022★ 1 cited
Categorifying computable reducibilities
Davide Trotta, Manlio Valenti, Valeria de Paiva
This paper presents categorical formulations of Turing, Medvedev, Muchnik, and Weihrauch reducibilities in Computability Theory, utilizing Lawvere doctrines. While the first notion…
math.CT2022★ 3 cited
Dialectica Principles via Gödel Doctrines
Davide Trotta, Matteo Spadetto, Valeria de Paiva
Gödel's Dialectica interpretation was conceived as a tool to obtain the consistency of Peano arithmetic via a proof of consistency of Heyting arithmetic in the 40s. In recent years…