Interactive Realizability and the elimination of Skolem functions in Peano Arithmetic

Federico Aschieri
(Lab. PPS, Paris 7)
Margherita Zorzi
(Laboratoire dÂÂ’Informatique de Paris-Nord)

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 our proof, we employ Interactive Realizability, a computational semantics for Peano Arithmetic which extends Kreisel's modified realizability to the classical case.

In Herman Geuvers and Ugo de'Liguoro: Proceedings Fourth Workshop on Classical Logic and Computation (CL&C 2012), Warwick, England, 8th July 2012, Electronic Proceedings in Theoretical Computer Science 97, pp. 1–18.
Published: 9th October 2012.

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