一种全Solovay可归约性与速度性概念的全化
A total Solovay reducibility and totalizing of the notion of speedability
AI总结：
本文引入全Solovay可归约性，证明Schnorr随机左c.e.实数在其下向上封闭，并通过全翻译函数定义全速度性，且不依赖加速常数选择。
摘要：
虽然Martin-Löf随机左c.e.实数的集合等于Solovay可归约性的最大度，Miyabe、Nies和Stephan（DOI:10.4115/jla.2018.10.3）已经证明左c.e. Schnorr随机实数在Solovay可归约性下不向上封闭。回顾对于两个左c.e.实数α和β，前者Solovay可归约于后者，如果存在一个部分可计算函数φ和常数c，使得对于所有有理数q < β，有α - φ(q) < c(β - q)。通过要求翻译函数φ是全的，我们引入了Solovay可归约性的全版本，它蕴含Schnorr可归约性。因此，根据Downey和Griffiths（DOI:10.2178/jsl/1082418542），Schnorr随机左c.e.实数的集合相对于全Solovay可归约性是向上封闭的。此外，我们观察到由Merkle和Titov（DOI:10.1007/978-3-030-50026-9_22）引入的速度性概念可以通过部分可计算翻译函数以类似于Solovay可归约性的方式等价刻画。通过要求翻译函数是全的，我们获得了全速度性的概念。与速度性一样，这一概念不依赖于加速常数的选择。
英文摘要：
While the set of Martin-Löf random left-c.e. reals is equal to the maximum degree of Solovay reducibility, Miyabe, Nies and Stephan(DOI:10.4115/jla.2018.10.3) have shown that the left-c.e. Schnorr random reals are not closed upwards under Solovay reducibility. Recall that for two left-c.e. reals~$α$ and~$β$, the former is Solovay reducible to the latter in case there is a partially computable function $φ$ and constant~$c$ such that for all rational numbers $q < β$ we have \[α- φ(q) < c(β- q).\] By requiring the translation function $φ$ to be total, we introduce a total version of Solovay reducibility that implies Schnorr reducibility. Accordingly, by Downey and Griffiths (DOI:10.2178/jsl/1082418542), the set of Schnorr random left-c.e. reals is closed upwards relative to total Solovay reducibility. Furthermore, we observe that the notion of speedability introduced by Merkle and Titov (DOI:10.1007/978-3-030-50026-9_22) can be equivalently characterized via partial computable translation functions in a way that resembles Solovay reducibility. By requiring the translation function to be total, we obtain the concept of total speedability. Like for speedability, this notion does not depend on the choice of the speeding constant.
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。
