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Eliminating Skolem Functions in Peano Arithmetic with Interactive Realizability

Federico Aschieri 1, Margherita Zorzi 2

(23/04/2012)

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.

1 :	PI.R2 (INRIA Paris - Rocquencourt)
	INRIA – Université Paris VII - Paris Diderot – CNRS : UMR7126
2 :	Laboratoire d'informatique de Paris-nord (LIPN)
	CNRS : UMR7030 – Université Paris XIII - Paris Nord

Domaine

:

Informatique/Logique en informatique

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Contributeur : Federico Aschieri <>

Soumis le : Lundi 23 Avril 2012, 01:06:11

Dernière modification le : Lundi 23 Avril 2012, 10:54:43