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

   
Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Independence results on the global structure of the Turing degrees


Authors: Marcia J. Groszek and Theodore A. Slaman
Journal: Trans. Amer. Math. Soc. 277 (1983), 579-588
MSC: Primary 03D30; Secondary 03E35
MathSciNet review: 694377
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: From CON(ZFC) we obtain: 1. CON$ ($ZFC$ + 2^\omega$ is arbitrarily large $ +$ there is a locally finite upper semilattice of size $ {\omega_2}$ which cannot be embedded into the Turing degrees as an upper semilattice).

2. CON$ ($ZFC$ + 2^\omega$ is arbitrarily large $ +$ there is a maximal independent set of Turing degrees of size $ {\omega _1}$).


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 03D30, 03E35

Retrieve articles in all journals with MSC: 03D30, 03E35


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0694377-4
PII: S 0002-9947(1983)0694377-4
Keywords: Turing degrees, forcing, uncountable embeddings, independent sets
Article copyright: © Copyright 1983 American Mathematical Society