Skip to main content

Applications of the low-basis theorem in arithmetic

  • Conference paper
  • First Online:
Recursion Theory Week

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1141))

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 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.95
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. D. Bean, "Effective coloration", Journal of Symbolic Logic, vol. 41, (1976), pp. 469–480.

    Article  MathSciNet  MATH  Google Scholar 

  2. P.G. Clote, "Anti-basis theorems and their relation to independence results in Peano arithmetic", in Model theory and arithmetic, Springer Lecture Notes in Mathematics, vol. 890, (1980), pp. 115–133.

    Article  MathSciNet  Google Scholar 

  3. P.G. Clote, "On recursive trees having a unique infinite branch", to appear in the Proceedings of the American Mathematical Society.

    Google Scholar 

  4. P.G. Clote, "Partition relations in arithmetic", to appear in the Proceedings of the Sixth International Latin American Symposium for Mathematical Logic, Caracas, (1983), 40 pages.

    Google Scholar 

  5. S. Fortune, D. Leivant, M. O'Donnell, "The expressiveness of simple and second order type structures", IBM Research Report RC 8542 (37221), October 31, 1980, 70 pages.

    Google Scholar 

  6. C.G. Jockusch, Jr., "Ramsey's theorem and recursive theory", Journal of Symbolic Logic, vol. 37, (1972), pp. 268–280.

    Article  MathSciNet  MATH  Google Scholar 

  7. M. Kaufmann, "On existence of Σn-end extensions", Logic Year 1979–80, Springer Lecture Notes in Mathematics, vol. 859, (1980), pp. 92–103.

    Article  MathSciNet  Google Scholar 

  8. L. Kirby and J. Paris, "Σn-collection schemas in arithmetic", Logic Colloquium '77, North Holland, Amsterdam, (1978), pp. 199–209.

    Google Scholar 

  9. E. Kranakis, "Partition and reflection properties of admissible ordinals", Annals of Mathematical Logic, vol. 22, (1982), pp. 213–242.

    Article  MathSciNet  MATH  Google Scholar 

  10. A. Máté, "Non-deterministic polynomial time computations and non-standard models of arithmetic", to appear in the JACM.

    Google Scholar 

  11. M. Löb and S. Wainer, "Hierarchies of number theoretic functions — part I", Archiv für Mathematische Logik und Grundlagenforschung, vol. 13, (1970), pp. 39–51, Part II in pp. 97–113.

    Article  MATH  Google Scholar 

  12. A. Manaster and J. Rosenstein, "Effective match-making (recursive theoretic aspects of a theorem of Philip Hall)", Proceedings of the London Mathematical Society, vol. 25, (1972).

    Google Scholar 

  13. K. McAloon, "Petri nets and large finite sets", Theoretical Computer Science, vol. 31 (1984), pp. 1–11.

    Article  MathSciNet  MATH  Google Scholar 

  14. J. Paris, "A hierarchy of cuts in models of arithemtic", Model theory of algebra and arithmetic (Proceedings, Karpacz, 1979), Lecture Notes in Mathematics, vol. 834, Springer Verlag, (1980), pp. 312–337.

    Article  MathSciNet  Google Scholar 

  15. J. Paris, "Some conservation results for fragments of arithmetic", Model theory and arithmetic, Springer Lecture Notes in Mathematics, vol. 890, (1980), pp. 251–262.

    Article  MathSciNet  Google Scholar 

  16. C. Parsons, Abstract in Notices of the American Mathematical Society, vol. 13, (1966), pp. 857–858.

    Google Scholar 

  17. R. Pino, "Πn-collection, indicatrices et ultrafiltres définissables", These de 3o cycle, Université Paris VII, (1983).

    Google Scholar 

  18. H. Putnam, "Trial and error predicates and the solution to a problem of Mostowski", Journal of Symbolic Logic, vol. 30, (1965), pp. 49–57.

    Article  MathSciNet  MATH  Google Scholar 

  19. J. Remmel, "On the effectiveness of the Schröder-Bernstein theorem", Proceedings of the American Mathematical Society, vol. 83, no. 2, (1981), pp. 379–386.

    MathSciNet  MATH  Google Scholar 

  20. U. Schöning, "A low and a high hierarchy within NP", Journal of Computer and System Sciences, vol. 26, (1983), 14 pages.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Heinz-Dieter Ebbinghaus Gert H. Müller Gerald E. Sacks

Rights and permissions

Reprints and permissions

Copyright information

© 1985 Springer-Verlag

About this paper

Cite this paper

Clote, P. (1985). Applications of the low-basis theorem in arithmetic. In: Ebbinghaus, HD., Müller, G.H., Sacks, G.E. (eds) Recursion Theory Week. Lecture Notes in Mathematics, vol 1141. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076215

Download citation

  • DOI: https://doi.org/10.1007/BFb0076215

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15673-4

  • Online ISBN: 978-3-540-39596-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics