Skip to main content

Anti-Basis theorems and their relation to independence results in Peano arithmetic

  • Conference paper
  • First Online:
Model Theory and Arithmetic

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 890))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. P. CLOTE: “Weak partition relations, finite games and independence results”, Proceedings of Logic Colloquium in Karpac 1979.

    Google Scholar 

  2. H. FRIEDMAN, K. Mc ALOON, S. SIMPSON: “A finite combinatorial principle which is equivalent to the 1-consistency of predicative analysis”.

    Google Scholar 

  3. C.G. JOCKUSCH, Jr.: “Ramsey's theorem and recursion theory”, SL 37-2, June 1972.

    Google Scholar 

  4. C.G. JOCKUSCH R. SOARE: “sk1/o classes and degrees of theories” Transactions of the American Mathematical Society 173, November 1972.

    Google Scholar 

  5. L.A.S. KIRBY, Ph. D. Thesis, Manchester University 1977.

    Google Scholar 

  6. L.A.S. KIRBY: “Flipping properties in arithmetic”. To appear.

    Google Scholar 

  7. L.A.S. KIRBY, J.B. PARIS: “Initial segments of models of Peano's axioms.

    Google Scholar 

  8. A. MACINTYRE: “Ramsey quantifiers in arithmetic” to appear.

    Google Scholar 

  9. A. MANASTER, J. ROSENSTEIN: “Effective matchmaking, rec. theor. aspects of a thm. of P. Hall”, Proc. London Math. Soc. 25 1972.

    Google Scholar 

  10. K. Mc ALOON: “Diagonal methods and strong cuts in models of arithmetic”, Logic Colloquium 1977, North Holland.

    Google Scholar 

  11. J.B. PARIS: “Some incompleteness results for Peano arithmetic, JSL.

    Google Scholar 

  12. J.B. PARIS: “A hierarchy of cuts in models of arithmetic.

    Google Scholar 

  13. P. PUDLAK: “Another combinatorial sentence independent of Peano's axioms” (unpublished).

    Google Scholar 

  14. C.E.M. YATES: “Arithmetical sets and retracing functions” Zeitschr. f. math. Logik und Grundlagen der Math. 13, 1967.

    Google Scholar 

Download references

Authors

Editor information

Chantal Berline Kenneth McAloon Jean-Pierre Ressayre

Rights and permissions

Reprints and permissions

Copyright information

© 1981 Springer-Verlag

About this paper

Cite this paper

Clote, P. (1981). Anti-Basis theorems and their relation to independence results in Peano arithmetic. In: Berline, C., McAloon, K., Ressayre, JP. (eds) Model Theory and Arithmetic. Lecture Notes in Mathematics, vol 890. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0095660

Download citation

  • DOI: https://doi.org/10.1007/BFb0095660

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11159-7

  • Online ISBN: 978-3-540-38629-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics