Skip to main content

Kleene degrees of ultrafilters

  • 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. A. Blass, Orderings of ultrafilters, Thesis, Harvard University, 1970.

    Google Scholar 

  2. _____, The Rudin-Keisler ordering of P-points, Trans. Amer. Math. Soc. 179 (1973) 145–166.

    MathSciNet  MATH  Google Scholar 

  3. _____, End extensions, conservative extensions, and the Rudin-Frolik ordering, Trans. Amer. Math. Soc. 225 (1977) 325–340.

    MathSciNet  MATH  Google Scholar 

  4. _____, A model-theoretic view of some special ultrafilters, in Logic Colloquium '77 (Proc. Wrocław) ed. A. Macintyre, L. Pacholski, J. Paris, North-Holland, 1978, 79–90.

    Google Scholar 

  5. _____, Selective ultrafilters and homogeneity, in preparation.

    Google Scholar 

  6. D. Booth, Ultrafilters on a countable set, Ann. Math. Logic 2 (1970) 1–24.

    Article  MathSciNet  MATH  Google Scholar 

  7. G. Choquet, Construction d'ultrafiltres sur N, Bull. Sci. Math. (2) 103 (1968) 41–48.

    MathSciNet  MATH  Google Scholar 

  8. _____, Deux classes remarquables d'ultrafiltres sur N, Bull. Sci. Math. (2) 103 (1958) 143–153.

    MathSciNet  MATH  Google Scholar 

  9. W. W. Comfort and S. Negrepontis, The Theory of Ultrafilters, Springer-Verlag, 1974.

    Google Scholar 

  10. L. Gillman and M. Jerison, Rings of Continuous Functions, Van Nostrand, 1960.

    Google Scholar 

  11. P. G. Hinman, Recursion-Theoretic Hierarchies, Springer-Verlag, 1978.

    Google Scholar 

  12. K. Kunen, Ultrafilters and independent sets, Trans. Amer. Math. Soc. 172 (1972) 299–306.

    Article  MathSciNet  MATH  Google Scholar 

  13. _____, Some points in βN, Math. Proc. Cambridge Phil. Soc. 80 (1976) 385–398.

    Article  MathSciNet  MATH  Google Scholar 

  14. _____, Weak P-points in N*, in Topology, vol. II (Proc. 4th Colloq., Budapest) ed. A. Császár, Colloq. Math. Soc. János Bolyai 23, North-Holland (1980) 741–750.

    Google Scholar 

  15. A. Louveau, Ultrafiltres sur N et derivation sequentelle, Bull. Sci. Math. 107 (1972) 353–382.

    MathSciNet  MATH  Google Scholar 

  16. A.R.D. Mathias, Happy families, Ann. Math. Logic 12 (1977) 59–111.

    Article  MathSciNet  MATH  Google Scholar 

  17. __________, O# and the p-point problem, in Higher Set Theory (Proc. Oberwolfach, 1977) ed. G. H. Műller and D.S. Scott, Springer Lecture Notes in Mathematics 669, 1978, 375–384.

    Google Scholar 

  18. A. Miller, There are no Q-points in Laver's model for the Borel Conjecture, Proc. Amer. Math. Soc. 78 (1980) 103–106.

    MathSciNet  MATH  Google Scholar 

  19. R.A. Pitt, The classification of ultrafilters on N, Thesis, University of Leicester, 1971.

    Google Scholar 

  20. F. P. Ramsey, On a problem of formal logic, Proc. London Math. Soc. (2) 30 (1929) 264–286.

    MathSciNet  MATH  Google Scholar 

  21. H. Rogers, Theory of Recursive Functions and Effective Computability, McGraw-Hill, 1967.

    Google Scholar 

  22. N. Rosen, Weakly Ramsey P points, Trans. Amer. Math. Soc. 269 (1982) 415–428.

    MathSciNet  MATH  Google Scholar 

  23. M.E. Rudin, Partial orders on the types of βN, Trans. Amer. Math. 155 (1971) 353–362.

    MathSciNet  MATH  Google Scholar 

  24. J. Silver, Every analytic set is Ramsey, J. Symbolic Logic 35 (1970) 60–64.

    Article  MathSciNet  MATH  Google Scholar 

  25. R.C. Solomon, private communication, April, 1972.

    Google Scholar 

  26. _____, A type of βN with N 0 relative types, Fund. Math. 79 (1973) 209–212.

    MathSciNet  Google Scholar 

  27. A. K. Steiner and E.F. Steiner, Relative types of points of βN/N, Trans. Amer. Math. Soc. 160 (1971) 279–286.

    MathSciNet  MATH  Google Scholar 

  28. E. Wimmers, The Shelah P-point independence theorem, Israel J. Math. 43 (1982) 28–48.

    Article  MathSciNet  MATH  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

Blass, A. (1985). Kleene degrees of ultrafilters. 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/BFb0076213

Download citation

  • DOI: https://doi.org/10.1007/BFb0076213

  • 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