Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-14T11:16:08.946Z Has data issue: false hasContentIssue false

Lowness for the class of random sets

Published online by Cambridge University Press:  12 March 2014

Antonín Kučera
Affiliation:
Department of Computer Science, Charles University, Malostranské Náměstí 25, 11800 Praha 1, Czech Republic, E-mail: [email protected]
Sebastiaan A. Terwijn
Affiliation:
Faculteit Wins/ILLC, Universiteit Van Amsterdam, Plantage Muidergracht 24, 1018 Tv Amsterdam, The Netherlands, E-mail: [email protected]

Abstract

A positive answer to a question of M. van Lambalgen and D. Zambella whether there exist nonrecursive sets that are low for the class of random sets is obtained. Here a set A is low for the class RAND of random sets if RAND = RANDA.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1999

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Gács, P., Every sequence is reducible to a random one, Inform. and Control, vol. 70 (1986), pp. 186192.CrossRefGoogle Scholar
[2]Kamae, T., Subsequences of normal sequences, Israel Journal of Mathematics, vol. 16 (1973), pp. 121149.CrossRefGoogle Scholar
[3]Kautz, S. M., Degrees of random sets, Ph.D. thesis, Cornell University, 1991.Google Scholar
[4]Kučera, A., Measure, -classes and complete extensions of PA, Recursion theory week 1984 (Ebbinghaus, H.-D., Müller, G.H., and Sacks, G.E., editors), Lecture Notes in Mathematics, vol. 1141, Springer-Verlag, 1985, pp. 245259.CrossRefGoogle Scholar
[5]Kučera, A., On relative randomness, Annals of Pure and Applied Logic, vol. 63 (1993), pp. 6167.CrossRefGoogle Scholar
[6]van Lambalgen, M., Random sequences, Ph.D. thesis, University of Amsterdam, 1987.Google Scholar
[7]van Lambalgen, M., The axiomatization of randomness, this Journal, vol. 55 (3) (1990), pp. 11431167.Google Scholar
[8]Martin-Löf, P., The definition of random sequences, Information and Control, vol. 9 (1966), pp. 602619.CrossRefGoogle Scholar
[9]Soare, R.I., Recursively enumerable sets and degrees, Springer-Verlag, 1987.CrossRefGoogle Scholar
[10]Terwijn, S.A. and Zambella, D., Algorithmic randomness and lowness, ILLC technical report ML-1997-07, University of Amsterdam, 1997.Google Scholar
[11]Zambella, D., On sequences with simple initial segments, ILLC technical report ML-1990-05, University of Amsterdam, 1990.Google Scholar