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Formalized recursive functionals and formalized realizability

About this Title

S. C. Kleene

Publication: Memoirs of the American Mathematical Society
Publication Year: 1969; Number 89
ISBNs: 978-0-8218-1289-1 (print); 978-1-4704-0038-5 (online)
DOI: https://doi.org/10.1090/memo/0089
MathSciNet review: 0244002

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Table of Contents

Chapters

  • Introduction
  • Part I. Formalized recursive functionals
  • 1. Computation tree numbers
  • 2. $p$-terms and $p$-functors; $r\simeq s$ (definition and basic properties)
  • 3. Representation of $p$-terms by proper indices
  • 4. The recursion theorem; the normal form theorem; $\{\tau \}[\alpha ]$ and $\wedge \alpha \, u[\alpha ]$; $!R \,\&\, [A(R)]$
  • Part II. Formalized realizability
  • 5. Intuitionistically provable formulas are realizable and $\bigcirc \!\!\!\!\!q$ -realizable