Degree spectra of the successor relation of computable linear orderings |
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Authors: | Jennifer Chubb Andrey Frolov Valentina Harizanov |
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Institution: | (1) Department of Mathematics, George Washington University, Washington, DC 20052, USA;(2) Department of Mechanics and Mathematics, Kazan State University, 420008 Kazan, Russia |
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Abstract: | We establish that for every computably enumerable (c.e.) Turing degree b the upper cone of c.e. Turing degrees determined by b is the degree spectrum of the successor relation of some computable linear ordering. This follows from our main result, that
for a large class of linear orderings the degree spectrum of the successor relation is closed upward in the c.e. Turing degrees.
The authors acknowledge partial support by the NSF binational grant DMS-0554841, and Harizanov by the NSF grant DMS-0704256,
and Chubb by the Sigma Xi Grant in Aid of Research. |
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 03C57 03D45 06A05 |
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