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arXiv · 1408.2282

On a conjecture of Dobrinen and Simpson concerning almost everywhere domination

Stephen Binns·Bjørn Kjos-Hanssen·Manuel Lerman·Reed Solomon
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Abstract

The notions of almost everywhere (a.e.) domination and its uniform version were introduced and studied in reverse mathematics. This paper studies these notions from a recursion-theoretic point of view and explore their connections to notions such as randomness and genericity. It is shown that if $Z$ is a.e. dominating then each $1$-$Z$-random is $2$-random. In other words, $0'\leq_{\rm LR} Z$ for every a.e. dominating $Z$, where ${\rm LR}$ denotes low-for-random reducibility. Other results and corollaries are also given.

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Stephen Binns, Bjørn Kjos-Hanssen, Manuel Lerman, Reed Solomon. 2014-08-10. On a conjecture of Dobrinen and Simpson concerning almost everywhere domination. https://doi.org/10.2178/jsl/1140641165

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