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Wiley InterScience | ||||||||
  DialecticaVolume 62 Issue 2, Pages 205 - 222 Special Issue: Special Issue: Gödel's dialectica Interpretation Published Online: 28 Jun 2008 Journal compilation © 2009 Editorial Board of dialectica
Abstract | References | Full Text: HTML, PDF (Size: 159K) | Related Articles | Citation Tracking  A Most Artistic Package of a Jumble of Ideas Copyright Journal compilation © 2008 Editorial Board of dialectica ABSTRACTIn the course of ten short sections, we comment on Gödel's seminal dialectica paper of fifty years ago and its aftermath. We start by suggesting that Gödel's use of functionals of finite type is yet another instance of the realistic attitude of Gödel towards mathematics, in tune with his defense of the postulation of ever increasing higher types in foundational studies. We also make some observations concerning Gödel's recasting of intuitionistic arithmetic via the dialectica interpretation, discuss the extra principles that the interpretation validates and comment on extensionality and higher order equality. The latter sections focus on the role of majorizability considerations within the dialectica and related interpretations for extracting computational information from ordinary proofs in mathematics. | 
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