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Extensional Gödel Functional Interpretation

A Consistensy Proof of Classical Analysis

  • Book
  • © 1973

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Authors:
  1. Horst Luckhardt
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 306)

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Table of contents (15 chapters)

  1. Front Matter

    Pages I-VI
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  2. Introduction and survey

    • Horst Luckhardt
    Pages 1-12

  3. A formal system of classical analysis

    • Horst Luckhardt
    Pages 13-27

  4. Elimination of extensionality

    • Horst Luckhardt
    Pages 28-40

  5. Translation of classical into intuitionistic approximated theories

    • Horst Luckhardt
    Pages 41-49

  6. Gödel's functional interpretation in the narrower sense

    • Horst Luckhardt
    Pages 50-58

  7. The calculus T of the primitive recursive functionals

    • Horst Luckhardt
    Pages 59-67

  8. Functional interpretation of classical arithmetic plus (ER)-qf, (AC)-qf and functional interpretation in the narrower sense of Heyting-analysis plus (ER)-qf, (MP), \((\underrightarrow V)\) in T

    • Horst Luckhardt
    Pages 68-75

  9. The calculus T⋃BR of the bar recursive functionals

    • Horst Luckhardt
    Pages 76-87

  10. Functional interpretation of classical (AC)o-, (ωAC)-analysis with (ER)-qf and functional interpretation in the narrower sense of Heyting-analysis plus (ER)-qf, (MP), \((\underrightarrow V),( \urcorner \Lambda \urcorner )^o ,(\mathop \omega \limits^{ \urcorner \urcorner } AC)\) in T⋃BR

    • Horst Luckhardt
    Pages 88-92

  11. Further consequences from the functional interpretation of classical analysis

    • Horst Luckhardt
    Pages 93-97

  12. Consistency proof by computation. Computation of T⋃BRo...o⋃μ

    • Horst Luckhardt
    Pages 98-119

  13. Generalized inductive definitions

    • Horst Luckhardt
    Pages 120-128

  14. Generalization of bar induction BID and the inductive generation processes to trees over species

    • Horst Luckhardt
    Pages 129-133

  15. A model for T⋃BR

    • Horst Luckhardt
    Pages 134-136

  16. On the bar recursive model of classical analysis and the general bar induction over species

    • Horst Luckhardt
    Pages 137-156

  17. Back Matter

    Pages 157-161
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Keywords

Bibliographic Information

  • Book Title: Extensional Gödel Functional Interpretation

  • Book Subtitle: A Consistensy Proof of Classical Analysis

  • Authors: Horst Luckhardt

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0060871

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1973

  • Softcover ISBN: 978-3-540-06119-9Published: 09 January 1973

  • eBook ISBN: 978-3-540-38283-6Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VI, 166

  • Topics: Analysis

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