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A Short Note on Spector’s Proof of Consistency of Analysis

  • Fernando Ferreira
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7318)

Abstract

In 1962, Clifford Spector gave a consistency proof of analysis using so-called bar recursors. His paper extends an interpretation of arithmetic given by Kurt Gödel in 1958. Spector’s proof relies crucially on the interpretation of the so-called numerical double negation shift principle. The argument for the interpretation is ad hoc. On the other hand, William Howard gave in 1968 a very natural interpretation of bar induction by bar recursion. We show directly that, within the framework of Gödel’s interpretation, numerical double negation shift is a consequence of bar induction.

Keywords

Intuitionistic Logic Proof Theory Peano Arithmetic Consistency Proof Characteristic Principle 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Fernando Ferreira
    • 1
  1. 1.Universidade de LisboaLisboaPortugal

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