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Computational randomness and lowness*

Published online by Cambridge University Press:  12 March 2014

Sebastiaan A. Terwijn  and
Domenico Zambella
Sebastiaan A. Terwijn
Affiliation:
Department of Mathematics and Computer Science, Free University of Amsterdam, de Boelelaan 1081 a, 1081 HV Amsterdam, The Netherlands, E-mail: terwijn@cs.vu.nl
Domenico Zambella
Affiliation:
Department of Mathematics, University of Torino, VIA Carlo Alberto 10, 10123 Torino, Italy, E-mail: domenico@dm.unito.it
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Abstract

We prove that there are uncountably many sets that are low for the class of Schnorr random reals. We give a purely recursion theoretic characterization of these sets and show that they all have Turing degree incomparable to 0′. This contrasts with a result of Kučera and Terwijn [5] on sets that are low for the class of Martin-Löf random reals.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 3 , September 2001 , pp. 1199 - 1205
Copyright
Copyright © Association for Symbolic Logic 2001

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Footnotes

*

Research supported by the Netherlands Foundation for Scientific Research (NWO) Project PGS 22-262. Most of this research was done while the authors were working at the University of Amsterdam.

References

REFERENCES

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