Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Turing incomparability in Scott sets


Authors: Antonín Kucera and Theodore A. Slaman
Journal: Proc. Amer. Math. Soc. 135 (2007), 3723-3731
MSC (2000): Primary 03D28
Published electronically: June 22, 2007
MathSciNet review: 2336589
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For every Scott set $ \mathcal F$ and every nonrecursive set $ X$ in $ \mathcal F$, there is a $ Y \in \mathcal F$ such that $ X$ and $ Y$ are Turing incomparable.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 03D28

Retrieve articles in all journals with MSC (2000): 03D28


Additional Information

Antonín Kucera
Affiliation: Department of Theoretical Computer Science and Mathematical Logic, Faculty of Mathematics and Physics, Charles University, Malostranské nám. 25, 118 00 Praha 1, Czech Republic
Email: kucera@ksi.mff.cuni.cz

Theodore A. Slaman
Affiliation: Department of Mathematics, The University of California, Berkeley, Berkeley, California 94720-3840
Email: slaman@math.berkeley.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08871-5
PII: S 0002-9939(07)08871-5
Keywords: Scott set, Turing degree, $K$-trivial, low for random
Received by editor(s): February 20, 2006
Received by editor(s) in revised form: August 14, 2006
Published electronically: June 22, 2007
Additional Notes: The first author was partially supported by the Research Project of the Ministry of Education of the Czech Republic MSM0021620838
The second author was partially supported by NSF grant DMS-0501167.
Communicated by: Julia Knight
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.



Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia