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|Title:||A join theorem for the computably enumerable degrees|
|Authors:||Jockusch Jr., C.G.|
|Keywords:||Computably enumerable degree|
|Source:||Jockusch Jr., C.G., Li, A., Yang, Y. (2004-07). A join theorem for the computably enumerable degrees. Transactions of the American Mathematical Society 356 (7) : 2557-2568. ScholarBank@NUS Repository. https://doi.org/10.1090/S0002-9947-04-03585-8|
|Abstract:||It is shown that for any computably enumerable (c.e.) degree w, if w ≠ 0, then there is a c.e. degree a such that (a ∨ w)′ = a″ = 0″ (so a is low 2 and a ∨ w is high). It follows from this and previous work of P. Cholak, M. Groszek and T. Slaman that the low and low 2 c.e. degrees are not elementarily equivalent as partial orderings.|
|Source Title:||Transactions of the American Mathematical Society|
|Appears in Collections:||Staff Publications|
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