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Journal of Logic and Computation Advance Access published online on August 17, 2009
Journal of Logic and Computation, doi:10.1093/logcom/exp041
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© The Author, 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Papers

Arithmetical Completeness of the Intuitionistic Logic of Proofs

Evgenij Dashkov

Department of Mathematical Logic and Theory of Algorithms, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow 119992, Russia.
E-mail: edashkov{at}gmail.com

Received 3 February 2009.


  Abstract

Classical logic of proofs LP naturally extends propositional calculus to the language enriched with formulas meaning t is a proof of formula F. Intuitionistic logic of proofs iLP introduced by Artemov and Iemhoff was conjectured to be complete with respect to intuitionistic arithmetic HA. The article presents a proof of this conjecture.

Keywords: Logic of proofs; intuitionistic arithmetic; admissible rules


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