A join theorem for the computably enumerable degrees

Please use this identifier to cite or link to this item: https://doi.org/10.1090/S0002-9947-04-03585-8

Title:	A join theorem for the computably enumerable degrees
Authors:	Jockusch Jr., C.G. Li, A. Yang, Y.
Keywords:	Computably enumerable degree Definable ideals Join theorem Turing jump
Issue Date:	Jul-2004
Citation:	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
URI:	http://scholarbank.nus.edu.sg/handle/10635/102663
ISSN:	00029947
DOI:	10.1090/S0002-9947-04-03585-8
Appears in Collections:	Staff Publications

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