Cofinal maximal chains in the Turing degrees

Wang, Wei; Wu, Liuzhen; Yu, Liang

doi:10.1090/S0002-9939-2014-11868-5

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 $\omega _1$”.

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