NDLI: On Pairs of Recursively Enumerable Degrees

Content Provider	Scilit
Author	Ambos-Spies, Klaus
Copyright Year	1984
Description	Lachlan and Yates proved that some, but not all, pairs of incomparable recursively enumerable (r.e.) degrees have an infimum. We answer some questions which arose from this situation. We show that not every nonzero incomplete r.e. degree is half of a pair of incomparable r.e. degrees which have an infimum, whereas every such degree is half of a pair without infimum. Further, we prove that every nonzero r.e. degree can be split into a pair of r.e. degrees which have no infimum, and every interval of r.e. degrees contains such a pair of degrees.
Related Links	https://www.ams.org/tran/1984-283-02/S0002-9947-1984-0737882-5/S0002-9947-1984-0737882-5.pdf
Ending Page	531
Page Count	25
Starting Page	507
ISSN	00029947
e-ISSN	10886850
DOI	10.2307/1999144
Journal	Transactions of the American Mathematical Society
Issue Number	2
Volume Number	283
Language	English
Publisher	Duke University Press
Publisher Date	1984-06-01
Access Restriction	Open
Subject Keyword	Logic Recursively Enumerable Infimum R.e Split Incomplete Yates Lachlan Answer
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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On Pairs of Recursively Enumerable Degrees