Cofinal maximal chains in the Turing degrees-Reference-Cited by-同舟云学术

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Cofinal maximal chains in the Turing degrees

Published:2014-01-30 Issue:4 Volume:142 Page:1391-1398
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Wang Wei,Wu Liuzhen,Yu Liang

Abstract

Assuming Z F C ZFC , we prove that C H CH holds if and only if there exists a cofinal maximal chain of order type ω 1 \omega _1 in the Turing degrees. However, it is consistent that Z F ZF +“the reals are not well ordered”+“there exists a cofinal chain in the Turing degrees of order type ω 1 \omega _1 ”.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2014-142-04/S0002-9939-2014-11868-5/S0002-9939-2014-11868-5.pdf

Reference9 articles.

1. Initial segments of the degrees of size ℵ₁;Abraham, Uri;Israel J. Math.,1986

2. Maximal chains in the Turing degrees;Chong, C. T.;J. Symbolic Logic,2007

3. Minimal degrees and the jump operator;Cooper, S. B.;J. Symbolic Logic,1973

4. Springer Monographs in Mathematics;Jech, Thomas,2003

5. Studies in Logic and the Foundations of Mathematics;Kunen, Kenneth,1983

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