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- W2344747119 abstract "An element $a$ of a lattice cups to an element $b > a$ if there is a $c < b$ such that $a cup c = b$. An element of a lattice has the cupping property if it cups to every element above it. We prove that there are non-zero honest elementary degrees that do not have the cupping property, which answers a question of Kristiansen, Schlage-Puchta, and Weiermann. In fact, we show that if $mathbf b$ is a sufficiently large honest elementary degree, then there is a non-zero honest elementary degree $mathbf a <_{mathrm E} mathbf b$ that does not cup to $mathbf b$. For comparison, we modify a result of Cai to show that in several versions of the related degrees of relative provability the preceding property holds for all non-zero $mathbf b$, not just sufficiently large $mathbf b$." @default.
- W2344747119 created "2016-06-24" @default.
- W2344747119 creator A5074399186 @default.
- W2344747119 date "2016-04-22" @default.
- W2344747119 modified "2023-09-27" @default.
- W2344747119 title "Honest elementary degrees and degrees of relative provability without the cupping property" @default.
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