{"title":"可数伯尔等价关系的树状图谱","authors":"Zhaoshen Zhai","doi":"arxiv-2409.09843","DOIUrl":null,"url":null,"abstract":"We present a streamlined exposition of a construction by R. Chen, A. Poulin,\nR. Tao, and A. Tserunyan, which proves the treeability of equivalence relations\ngenerated by any locally-finite Borel graph such that each component is a\nquasi-tree. More generally, we show that if each component of a locally-finite\nBorel graph admits a finitely-separating Borel family of cuts, then we may\n'canonically' construct a forest of special ultrafilters; moreover, if the cuts\nare dense towards ends, then this forest is a Borel treeing.","PeriodicalId":501306,"journal":{"name":"arXiv - MATH - Logic","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Tree-like graphings of countable Borel equivalence relations\",\"authors\":\"Zhaoshen Zhai\",\"doi\":\"arxiv-2409.09843\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present a streamlined exposition of a construction by R. Chen, A. Poulin,\\nR. Tao, and A. Tserunyan, which proves the treeability of equivalence relations\\ngenerated by any locally-finite Borel graph such that each component is a\\nquasi-tree. More generally, we show that if each component of a locally-finite\\nBorel graph admits a finitely-separating Borel family of cuts, then we may\\n'canonically' construct a forest of special ultrafilters; moreover, if the cuts\\nare dense towards ends, then this forest is a Borel treeing.\",\"PeriodicalId\":501306,\"journal\":{\"name\":\"arXiv - MATH - Logic\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Logic\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.09843\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Logic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.09843","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
我们对 R. Chen、A. Poulin、R. Tao 和 A. Tserunyan 的构造进行了精简阐述。Tao, and A. Tserunyan 的构造，该构造证明了由任何局部有限伯尔图生成的等价关系的可树性，且每个分量都是水树。更广义地说，我们证明了如果局部有限伯尔图的每个分量都有一个有限分离的伯尔切分族，那么我们就可以 "规范地 "构造一个特殊超滤波器森林；此外，如果切分向两端密集，那么这个森林就是伯尔树化。
Tree-like graphings of countable Borel equivalence relations
We present a streamlined exposition of a construction by R. Chen, A. Poulin,
R. Tao, and A. Tserunyan, which proves the treeability of equivalence relations
generated by any locally-finite Borel graph such that each component is a
quasi-tree. More generally, we show that if each component of a locally-finite
Borel graph admits a finitely-separating Borel family of cuts, then we may
'canonically' construct a forest of special ultrafilters; moreover, if the cuts
are dense towards ends, then this forest is a Borel treeing.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
