Skip Navigation


Journal of Logic and Computation Advance Access originally published online on October 1, 2008
Journal of Logic and Computation 2009 19(1):151-158; doi:10.1093/logcom/exn032
This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Kalimullin, I.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author, 2008. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

This article appears in the following Journal of Logic and Computation issue: Special Issue: Logic and Computation in the Real World: CiE 2007 [View the issue table of contents]

Original Articles

Enumeration Degrees and Enumerability of Familes

Iskander Kalimullin *

Kazan State University, Kazan, 420008, Kremlevskaya str. 18, Russia.
E-mail: Iskander.Kalimullin{at}ksu.ru

Received 9 January 2008.

We study the enumerability of families relative to the enumeration degrees. It is shown that if a family of finite sets is e-reducible to every non-zero e-degree, then the family is computably enumerable (c.e). On the another hand, we will find a non-c.e. family which is e-reducible to all non-zero e-degree. This allows to construct a model, whose (extended) degree spectrum coincides with the non-zero e-degrees.

Keywords: c.e. Families; turing degrees; e-degrees (enumeration degrees); degree spectra of models

*Supported by RFBR grant 05-01-00605 and President RF grant MK-4314.2008.1



References

  1. Cooper SB. Computability Theory. (2004) 26. UK: University of Leeds, Chapman&Hall/CRC. 424.
  2. Gutteridge L. Some Results on Enumeration Reducibility. (1971) Simon Fraser University. PhD Thesis.
  3. Rogers H Jr. Theory of Recursive Functions and Effective Computability. (1967) New York: McGraw-Hill Book Company.
  4. Selivanov VL. On index sets of computable classes of finite sets. In. In: Algorithms and Automatas.—Arslanov MM, ed. (1978) Kazan. 95–99. (In Russian).
  5. Slaman TA. Relative to any nonrecursive set. Proceedings of the American Mathematical Society (1998) 126:2117–2122.[CrossRef][Web of Science]
  6. Soskov IN. Degree spectra and co-spectra of structures. Annual of University Sofia (2004) 96:45–68.
  7. Wehner S. Enumerations, countable structures, and Turing degrees. Proceedings of the American Mathematical Society (1998) 126:2131–2139.[CrossRef][Web of Science]

Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?



This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Kalimullin, I.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?