2012/10/11 by Federico Aschieri, Margherita Zorzi
Computer Science · #cs.LO
paper · pdf · doi:10.4204/eptcs.97.1
published as EPTCS 97, 2012, pp. 1-18 · In Proceedings CL&C 2012, arXiv:1210.2890
arxiv created 2012/10/11 · arxiv updated 2012/10/12
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.