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Dialectica Principles via Gödel Doctrines
Gödel’s Dialectica interpretation was conceived as a tool to obtain the consistency of Heyting arithmetic in the 40s. In recent …
Davide Trotta
,
Matteo Spadetto
,
Valeria de Paiva
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A characterization of generalized existential completions
This paper aims to provide an intrinsic characterization of the notion of generalized existential completion of a conjunctive doctrine …
Maria Emilia Maietti
,
Davide Trotta
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Dialectica logical principles: not only rules
Gödel’s Dialectica interpretation was designed to obtain the consistency of Peano arithmetic via a proof of consistency of …
Davide Trotta
,
Matteo Spadetto
,
Valeria de Paiva
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Dialectica logical principles
Gödel’s Dialectica interpretation was designed to obtain a relative consistency proof for Heyting arithmetic, to be used in …
Davide Trotta
,
Matteo Spadetto
,
Valeria de Paiva
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The Gödel fibration
We introduce the notion of a Gödel fibration, which is a fibration categorically embodying both the logical principles of traditional …
Davide Trotta
,
Matteo Spadetto
,
Valeria de Paiva
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The existential completion
We determine the existential completion of a primary doctrine, and we prove that the 2-monad obtained from it is lax-idempotent, and …
Davide Trotta
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