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Functional interpretation and the existence property

Klaus Jørgensen

Mathematical Logic Quarterly 50 (6):573-576 (2004)

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Functional interpretations of constructive set theory in all finite types.Justus Diller - 2008 - Dialectica 62 (2):149–177.details Gödel's dialectica interpretation of Heyting arithmetic HA may be seen as expressing a lack of confidence in our understanding of unbounded quantification. Instead of formally proving an implication with an existential consequent or with a universal antecedent, the dialectica interpretation asks, under suitable conditions, for explicit 'interpreting' instances that make the implication valid. For proofs in constructive set theory CZF-, it may not always be possible to find just one such instance, but it must suffice to explicitly name a set (...) Download Export citation Bookmark 1 citation
Proof interpretations with truth.Jaime Gaspar & Paulo Oliva - 2010 - Mathematical Logic Quarterly 56 (6):591-610.details This article systematically investigates so-called “truth variants” of several functional interpretations. We start by showing a close relation between two variants of modified realizability, namely modified realizability with truth and q-modified realizability. Both variants are shown tobe derived from a single “functional interpretation with truth” of intuitionistic linear logic. This analysis suggests that several functional interpretations have truth and q-variants. These variants, however, require a more involved modification than the ones previously considered. Following this lead we present truth and q-variants (...) Download Export citation Bookmark 1 citation
Gödel's functional interpretation and its use in current mathematics.Ulrich Kohlenbach - 2008 - Dialectica 62 (2):223–267.details Download Export citation Bookmark 1 citation

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