Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 
 

 

Cofinal maximal chains in the Turing degrees


Authors: Wei Wang, Liuzhen Wu and Liang Yu
Journal: Proc. Amer. Math. Soc. 142 (2014), 1391-1398
MSC (2010): Primary 03D28, 03E25
DOI: https://doi.org/10.1090/S0002-9939-2014-11868-5
Published electronically: January 30, 2014
MathSciNet review: 3162259
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Assuming $ ZFC$, we prove that $ CH$ holds if and only if there exists a cofinal maximal chain of order type $ \omega _1$ in the Turing degrees. However, it is consistent that $ ZF$+``the reals are not well ordered''+``there exists a cofinal chain in the Turing degrees of order type $ \omega _1$''.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 03D28, 03E25

Retrieve articles in all journals with MSC (2010): 03D28, 03E25


Additional Information

Wei Wang
Affiliation: Institute of Logic and Cognition and Department of Philosophy, Sun Yat-sen University, 135 Xingang Xi Road, Guangzhou 510275, People’s Republic of China
Email: wwang.cn@gmail.com

Liuzhen Wu
Affiliation: Kurt Gödel Research Center for Mathematical Logic, University of Vienna, Währinger Strasse 25, A-1090 Vienna, Austria
Email: liu.zhen.wu@univie.ac.at

Liang Yu
Affiliation: Institute of Mathematics, Nanjing University, 22 Hankou Road, Nanjing 210093, People’s Republic of China
Email: yuliang.nju@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2014-11868-5
Keywords: Turing degrees, maximal chains
Received by editor(s): October 1, 2011
Received by editor(s) in revised form: November 11, 2011, April 14, 2012, and May 13, 2012
Published electronically: January 30, 2014
Additional Notes: The first author was partially supported by NSFC Grant 11001281 of China and an NCET grant from MOE of China.
The second author was supported by FWF Project P23316.
The third author was partially supported by NSFC grant No. 11071114 and a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.
Communicated by: Julia Knight
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.