David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Notre Dame Journal of Formal Logic 50 (4):469-493 (2009)
Semi-hyperhypersimple c.e. sets, also known as diagonals, were introduced by Kummer. He showed that by considering an analogue of hyperhypersimplicity, one could characterize the sets which are the Halting problem relative to arbitrary computable numberings. One could also consider half of splittings of maximal or hyperhypersimple sets and get another variant of maximality and hyperhypersimplicity, which are closely related to the study of automorphisms of the c.e. sets. We investigate the Turing degrees of these classes of c.e. sets. In particular, we show that the analogue of a theorem of Martin fails for these classes
|Keywords||maximal hyperhypersimple computable numberings|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Tamara Hummel & Carl G. Jockusch Jr (1999). Generalized Cohesiveness. Journal of Symbolic Logic 64 (2):489-516.
Michael Stob (1983). Wtt-Degrees and T-Degrees of R.E. Sets. Journal of Symbolic Logic 48 (4):921-930.
Slawomir Solecki (1994). Covering Analytic Sets by Families of Closed Sets. Journal of Symbolic Logic 59 (3):1022-1031.
Jeanleah Mohrherr (1983). Kleene Index Sets and Functional M-Degrees. Journal of Symbolic Logic 48 (3):829-840.
Johanna N. Y. Franklin & Frank Stephan (2010). Van Lambalgen's Theorem and High Degrees. Notre Dame Journal of Formal Logic 52 (2):173-185.
Andrew Arana (2001). Solovay's Theorem Cannot Be Simplified. Annals of Pure and Applied Logic 112 (1):27-41.
André Nies, Frank Stephan & Sebastiaan A. Terwijn (2005). Randomness, Relativization and Turing Degrees. Journal of Symbolic Logic 70 (2):515 - 535.
John T. Gill Iii & Paul H. Morris (1974). On Subcreative Sets and S-Reducibility. Journal of Symbolic Logic 39 (4):669 - 677.
Frank Stephan (2001). On the Structures Inside Truth-Table Degrees. Journal of Symbolic Logic 66 (2):731-770.
Su Gao (1994). The Degrees of Conditional Problems. Journal of Symbolic Logic 59 (1):166-181.
Tamara Lakins Hummel (1994). Effective Versions of Ramsey's Theorem: Avoiding the Cone Above 0'. Journal of Symbolic Logic 59 (4):1301-1325.
Marcia J. Groszek, Michael E. Mytilinaios & Theodore A. Slaman (1996). The Sacks Density Theorem and Σ2-Bounding. Journal of Symbolic Logic 61 (2):450 - 467.
Donald A. Martin (1963). A Theorem on Hyperhypersimple Sets. Journal of Symbolic Logic 28 (4):273-278.
Manuel Lerman (1970). Turing Degrees and Many-One Degrees of Maximal Sets. Journal of Symbolic Logic 35 (1):29-40.
Sorry, there are not enough data points to plot this chart.
Added to index2010-09-13
Total downloads1 ( #598,352 of 1,696,508 )
Recent downloads (6 months)1 ( #342,645 of 1,696,508 )
How can I increase my downloads?