Archive for Mathematical Logic

, Volume 27, Issue 2, pp 149–160 | Cite as

Equivalence of bar recursors in the theory of functionals of finite type

  • Marc Bezem
Article
Received:

Abstract

The main result of this paper is the equivalence of several definition schemas of bar recursion occurring in the literature on functionals of finite type. We present the theory of functionals of finite type, in [T] denoted byqf-WE-HAω, which is necessary for giving the equivalence proofs. Moreover we prove two results on this theory that cannot be found in the literature, namely the deduction theorem and a derivation of Spector's rule of extensionality from [S]: ifP→T1=T2 and Q[X∶≡T1], then P→Q[X∶≡ T2], from the at first sight weaker rule obtained by omitting “P→”.

Keywords

Mathematical Logic Finite Type Deduction Theorem Equivalence Proof Definition Schema 
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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Marc Bezem
    • 1
  1. 1.Centre for Mathematics and Computer ScienceAB AmsterdamThe Netherlands

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