Eliminating Skolem Functions in Peano Arithmetic with Interactive Realizability
Résumé
We present a new syntactical proof that first-order Peano Arithmetic with Skolem axioms is conservative over Peano Arithmetic alone for arithmetical formulas. This result -- which shows that the Excluded Middle principle can be used to eliminate Skolem functions -- has been previously proved by other techniques, among them the epsilon substitution method and forcing. In this paper, we employ Interactive Realizability, a computational semantics for Peano Arithmetic which extends Kreisel's modified realizability to the classical case.
Domaines
Logique en informatique [cs.LO]
Origine : Fichiers produits par l'(les) auteur(s)
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