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Interactive Realizability and the elimination of Skolem functions in Peano Arithmetic

Author(s): Federico Aschieri | Margherita Zorzi

Journal: Electronic Proceedings in Theoretical Computer Science
ISSN 2075-2180

Volume: 97;
Issue: Proc. CL;
Start page: 1;
Date: 2012;
Original page

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.
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