逻辑博客2020

摘要：

今年的博客集中在群论与逻辑和算法的联系上。第一篇文章是关于自动机可呈现的组。然后有几个职位相关的拓扑群，例如伊万诺夫和Majcher表明，极端顺从性的闭子群的$S_\infty$是一个博雷尔财产。Harrison-Trainor和Nies的一篇文章回顾了Segal关于伪有限群的笔记，并尝试了一个有效的版本。大约25%是关于可计算性和随机性的，特别是Greenberg，Nies和Turetsky在K-trivials上比图灵弱的可约性的等价性，以及Nies和Tomamichel在量子环境中的有效SMB定理。

英文摘要：

This year's blog has focused on the connections of group theory with logic and algorithms. The first post is on automata presentable groups. Then there are several posts related to topological groups, for instance Ivanov and Majcher showing that extreme amenability of closed subgroups of $S_\infty$ is a Borel property. One post due to Harrison-Trainor and Nies reviews notes by Segal on pseudofinite groups, and attempts an effective version. About 25 percent is on computability and randomness, in particular equivalence of reducibilities weaker than Turing on the K-trivials by Greenberg, Nies and Turetsky, and the effective SMB theorem in the quantum setting by Nies and Tomamichel.

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。