关于Dobrinen和Simpson关于几乎处处控制的一个猜想
On a conjecture of Dobrinen and Simpson concerning almost everywhere domination
摘要：
几乎处处（a.e.）摘要在逆向数学中引入并研究了控制及其一致形式。本文从递归理论的角度研究这些概念，并探讨它们与随机性和泛型等概念的联系。证明了如果$Z$是a. e.支配，则每个$1$ - $Z$ -随机是$2$ -随机。换句话说，$0'\leq_{\rm LR} Z$每个a.e.主导$Z$，其中${\rm LR}$表示低随机约简。并给出了其它结果和推论。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
