Cofinal maximal chains in the Turing degrees
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- by Wei Wang, Liuzhen Wu and Liang Yu PDF
- Proc. Amer. Math. Soc. 142 (2014), 1391-1398 Request permission
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
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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
- MR Author ID: 1051075
- 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
- MR Author ID: 725077
- Email: yuliang.nju@gmail.com
- 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
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 3162259