Interactive Realizability and the elimination of Skolem functions in   Peano Arithmetic
  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. 
Federico Aschieri (Lab. PPS, Paris 7), Margherita Zorzi (Laboratoire   d\^A'Informatique de Paris-Nord)
cs.LO