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On Krivine's Realizability Interpretation of Classical Second-Order Arithmetic

Oliva P., Streicher T.

Fundamenta Informaticae

2008

Vol. 84, nr 2

207-220

This article investigates Krivine's realizability interpretation of classical second-order arithmetic and its recent extension handling countable choice. We will start by presenting a two-step interpretation which first eliminates classical logic via a negative translation and then applies standard realizability interpretation. We then argue that a slight variant of Krivine's interpretation corresponds to this two-step interpretation. This variant can be viewed as the continuation passing style variant of Krivine's original interpretation, and as such uses standard l-terms and avoids the use of new continuation constants in the interpretation of classical logic.