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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Two theorems on truth table degrees


Author: R. G. Downey
Journal: Proc. Amer. Math. Soc. 103 (1988), 281-287
MSC: Primary 03D30; Secondary 03D25
MathSciNet review: 938684
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Abstract: In this article we solve two questions of Odifreddi on the r.e. $ {\text{tt}}$-degrees. First we construct an r.e. $ {\text{tt}}$-degree with anticupping property. In fact, we construct r.e. $ {\text{tt}}$-degrees $ {\mathbf{a}},{\mathbf{b}}$ with $ {\mathbf{0}} < {\mathbf{a}} < {\mathbf{b}}$ and such that for all (not necessarily r.e.) $ {\text{tt}}$-degrees $ {\mathbf{c}}$ if $ {\mathbf{a}} \cup {\mathbf{c}} \geq {\mathbf{b}}$ then $ {\mathbf{a}} \leq {\mathbf{c}}$. This result also has ramifications in, for example, the r.e. $ {\text{wtt}}$-degrees. Finally we solve another question of Odifreddi by constructing an r.e. $ {\text{tt}}$-degree with no greatest r.e. $ m$-degree.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0938684-6
PII: S 0002-9939(1988)0938684-6
Keywords: Global anticupping property, truth table degrees, $ m$-degrees
Article copyright: © Copyright 1988 American Mathematical Society