Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/142298
Title: Degrees containing members of thin II1 classes are dense and co-dense
Authors: Downey, Rodney G.
Wu, Guohua
Yang, Yue
Keywords: Science::Mathematics
Issue Date: 2018
Source: Downey, R. G., Wu, G., & Yang, Y. (2018). Degrees containing members of thin II1 classes are dense and co-dense. Journal of Mathematical Logic, 18(1), 1850001-. doi:10.1142/S0219061318500010
Journal: Journal of Mathematical Logic
Abstract: In [Countable thin II1 classes, Ann. Pure Appl. Logic 59 (1993) 79-139], Cenzer, Downey, Jockusch and Shore proved the density of degrees (not necessarily c.e.) containing members of countable thin II1 classes. In the same paper, Cenzer et al. also proved the existence of degrees containing no members of thin II1 classes. We will prove in this paper that the c.e. degrees containing no members of thin II1 classes are dense in the c.e. degrees. We will also prove that the c.e. degrees containing members of thin II1 classes are dense in the c.e. degrees, improving the result of Cenzer et al. mentioned above. Thus, we obtain a new natural subclass of c.e. degrees which are both dense and co-dense in the c.e. degrees, while the other such class is the class of branching c.e. degrees (See [P. Fejer, The density of the nonbranching degrees, Ann. Pure Appl. Logic 24 (1983) 113-130] for nonbranching degrees and [T. A. Slaman, The density of infima in the recursively enumerable degrees.
URI: https://hdl.handle.net/10356/142298
ISSN: 0219-0613
DOI: 10.1142/S0219061318500010
Rights: © 2018 World Scientific Publishing Company.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

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