Skip to main content

Randomness and generalizations of fixed point free functions

Part of the Lecture Notes in Mathematics book series (LNM,volume 1432)

Keywords

  • Measure Zero
  • Recursive Function
  • Recursion Theory
  • Turing Degree
  • Recursive Sequence

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M.M. Arslanov (1981) On some generalizations of the theorem on fixed points, Izv. Vyssh. Uchebn. Zaved. Mat. 228, No 5, 9–16 (Russian).

    MathSciNet  Google Scholar 

  2. M.M. Arslanov, R.F. Nadirov, V.D. Solov'ev (1977) Completeness criteria for recursively enumerable sets and some general theorems on fixed points, Izv. Vyssh. Uchebn. Zaved. Mat. 179, No 4, 3–7, (Russian).

    Google Scholar 

  3. G.J.Chaitin (1977) Algorithmic information theory, IBM Journal of Research and Development, July 1977, 350–359.

    Google Scholar 

  4. O. Demuth (1975) On constructive pseudonumbers, Comment. Math. Univ. Carolinae 16, 315–331 (Russian).

    MathSciNet  Google Scholar 

  5. O. Demuth (1982) On some classes of arithmetical real numbers, Comment. Math. Univ. Carolinae 23, 453–465 (Russian).

    MathSciNet  MATH  Google Scholar 

  6. C.G.Jockusch, Jr., M.Lerman, R.I.Soare, R.M.Solovay (1989) Recursively enumerable sets modulo iterated jumps and extensions of Arslanov's completeness criterion, to appear in J. Symbolic Logic.

    Google Scholar 

  7. C.G. Jockusch, Jr., R.A. Shore (1984) Pseudo jump operators. II: Transfinite iterations, hierarchies, and minimal covers, J. Symbolic Logic 49, 1205–1236.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. C.G. Jockusch,Jr., R.I. Soare (1972) Π 01 classes and degrees of theories, Trans. Amer. Math. Soc. 173, 33–56.

    MathSciNet  MATH  Google Scholar 

  9. C.G. Jockusch,Jr., R.I. Soare (1972) Degrees of members of Π 01 classes, Pacific J. Math., 40, 605–616.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. A.Kučera (1985) Measure Π 01 -classes and complete extensions of PA, In: Recursion Theory Week, Proceedings (Ebbinghaus, Müller, Sacks editors), Lect. Notes in Math. No. 1141, Springer-Verlag, 245–259.

    Google Scholar 

  11. A.Kučera (1986) An alternative, priority-free, solution to Post's problem, In: Proceedings, MFCS'86 (Gruska, Rovan, Wiedermann editors.), Lect. Notes in Comp. Science, No. 233, Springer-Verlag, 493–500.

    Google Scholar 

  12. A.Kučera (1989) On the use of diagonally nonrecursive functions, In: Proceedings, Logic Colloquium'87 (Ebbinghaus et al. editors), North-Holland, 219–239.

    Google Scholar 

  13. S.A.Kurtz (1981) Randomness and genericity in the degrees of unsolvability, PhD thesis, Univ. of Illinois at Urbana-Champaign.

    Google Scholar 

  14. S.A.Kurtz (ta) A note on random sets, to appear.

    Google Scholar 

  15. P. Martin-Löf (1966) The definition of random sequences, Information and Control, 9, 602–619.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. G.E. Sacks (1963) Degrees of unsolvability, Annals of Math. Studies 55, Princeton University Press, Princeton, N.J.

    MATH  Google Scholar 

  17. R.I.Soare (1987) Recursively enumerable sets and degrees: A study of computable functions and computably generated sets, Springer-Verlag.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1990 Springer-Verlag

About this paper

Cite this paper

Kučera, A. (1990). Randomness and generalizations of fixed point free functions. In: Ambos-Spies, K., Müller, G.H., Sacks, G.E. (eds) Recursion Theory Week. Lecture Notes in Mathematics, vol 1432. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086121

Download citation

  • DOI: https://doi.org/10.1007/BFb0086121

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52772-5

  • Online ISBN: 978-3-540-47142-4

  • eBook Packages: Springer Book Archive