Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/142298
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dc.contributor.authorDowney, Rodney G.en_US
dc.contributor.authorWu, Guohuaen_US
dc.contributor.authorYang, Yueen_US
dc.date.accessioned2020-06-18T07:56:49Z-
dc.date.available2020-06-18T07:56:49Z-
dc.date.issued2018-
dc.identifier.citationDowney, 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/S0219061318500010en_US
dc.identifier.issn0219-0613en_US
dc.identifier.urihttps://hdl.handle.net/10356/142298-
dc.description.abstractIn [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.en_US
dc.description.sponsorshipMOE (Min. of Education, S’pore)en_US
dc.language.isoenen_US
dc.relation.ispartofJournal of Mathematical Logicen_US
dc.rights© 2018 World Scientific Publishing Company.en_US
dc.subjectScience::Mathematicsen_US
dc.titleDegrees containing members of thin II1 classes are dense and co-denseen_US
dc.typeJournal Articleen
dc.contributor.schoolSchool of Physical and Mathematical Sciencesen_US
dc.identifier.doi10.1142/S0219061318500010-
dc.identifier.scopus2-s2.0-85038924728-
dc.identifier.issue1en_US
dc.identifier.volume18en_US
dc.subject.keywordsΠ10 Classesen_US
dc.subject.keywordsTuring Degreesen_US
item.fulltextNo Fulltext-
item.grantfulltextnone-
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