Simple proof of the completeness theorem for second-order classical and intuitionistic logic by reduction to first-order mono-sorted logic

Authors:
Karim Nour;Christophe Raffalli
Affiliations:
Campus Scientifique LAMA--Equipe de Logique, Université de Chambéry, 73376 Le Bourget du Lac, France;Campus Scientifique LAMA--Equipe de Logique, Université de Chambéry, 73376 Le Bourget du Lac, France
Venue:
Theoretical Computer Science
Year:
2003

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Abstract

We present a simpler way than usual to deduce the completeness theorem for the second-order classical logic from the first-order one. We also extend our method to the case of second-order intuitionistic logic.