Two theorems on truth table degrees
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- by R. G. Downey PDF
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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.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 281-287
- MSC: Primary 03D30; Secondary 03D25
- DOI: https://doi.org/10.1090/S0002-9939-1988-0938684-6
- MathSciNet review: 938684