Definition
In proof theory, the Dialectica interpretation is a proof interpretation of intuitionistic logic into a finite type extension of primitive recursive arithmetic, the so-called System T. It was developed by Kurt Gödel to provide a consistency proof of arithmetic. The name of the interpretation comes from the journal Dialectica, where Gödel's paper was published in a 1958 special issue dedicated to Paul Bernays on his 70th birthday.
Related concepts
Affine logicAnne S. TroelstraAxiom of choiceBar recursionConsistencyConsistency proofDialecticaDialectica spacesFinitismGödel's incompleteness theoremGödel–Gentzen negative translationHeyting arithmeticHigher-order functionIndependence of premiseIntuitionistic logicJean-Yves GirardJeremy AvigadJoseph R. ShoenfieldKurt GödelLinear logicLogic translationMarkov's principleMathematical inductionPaul BernaysPeano arithmeticPrimitive recursive arithmeticPrimitive recursive functionalProof theorySamuel BussSolomon FefermanUlrich KohlenbachValeria de PaivaWeak Kőnig's lemma
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