Lowness and Π20 Nullsets

Journal of Symbolic Logic

Volumn 71, Issue 3, 2006, Pages 1044-1052

  Downey, Rod ^a   Nies, Andre ^b   Weber, Rebecca ^c   Yu, Liang ^d  

^a VICTORIA UNIVERSITY OF WELLINGTON   (New Zealand)

^b UNIVERSITY OF AUCKLAND   (New Zealand)

^c Lamont Doherty Earth Observatory   (United States)

^d NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33748523478     PISSN: 00224812     EISSN: None     Source Type: Journal    
DOI: 10.2178/jsl/1154698590     Document Type: Article

References (16)

1. R. DOWNEY, E. GRIFFITHS, and S. REID, On Kurtz randomness, Theoretical Computer Science, vol. 321 (2004), pp. 249-270.
2. R. DOWNEY and D. HIRSCHFELDT, Algorithmic Randomness and Complexity, Springer-Verlag, to appear. Current version available at http://www.mes.vuw.ac. nz/~downey.
3. S. FIGUEIRA, A. NIES, and F. STEPHAN, Lowness properties and approximations of the jump, Proceedings of the Workshop of Logic, Language, Information and Computation (WoLLIC), 2005, Electronic Lecture Notes in Theoretical Computer Science, vol. 143(2006), pp. 45-57.
4. P. GÁCS, Every set is reducible to a random one, Information and Control, vol. 70 (1986), pp. 186-192.
5. H. GAIFMAN and M. SNIR, Probabilities over rich languages, testing and randomness, this JOURNAL, vol. 47 (1982), pp. 495-548.
6. S. KAUTZ, Degrees of random sets, Ph.D. thesis, Cornell University, 1991.
7. S. KURTZ, Randomness and genericity in the degrees of unsolvability, Ph.D. thesis, University of Illinois at Urbana-Champaign, 1981.
8. 0, classes, and complete extensions of PA, Lecture Notes in Mathematics, vol. 1141, Springer, 1985, pp. 245-259.
9. A. KUČERA and S. TERWIJN, Lowness for the class of random sets, this JOURNAL, vol. 64 (1999), no. 4, pp. 1396-1402.
10. P. MARTIN-LÖF, The definition of random sequences. Information and Control, vol. 9 (1966), pp. 602-619.
11. A. NIES, Computability and Randomness, to appear.
12. _, Low for random sets: The story, preprint, available at http://www.cs.auckland.ac.nz/~nies.
13. _, Non-cupping and randomness. Proceedings of the American Mathematical Society, to appear.
14. G. SACKS, Degrees of Unsolvability, Princeton University Press, 1963.
15. F. STEPHAN, personal communication.
16. Y. WANG. Randomness and Complexity, Ph.D. thesis, University of Heidelberg, 1996.