{"title":"阿贝尔群纯短精确序列展开中分叉和分割的转移原理","authors":"Akash Hossain","doi":"arxiv-2409.10148","DOIUrl":null,"url":null,"abstract":"In their article about distality in valued fields, Aschenbrenner, Chernikov,\nGehret and Ziegler proved resplendent Ax-Kochen-Ershov principles for\nquantifier elimination in pure short exact sequences of Abelian structures. We\nstudy how their work relates to forking, and we prove Ax-Kochen-Ershov\nprinciples for forking and dividing in this setting.","PeriodicalId":501306,"journal":{"name":"arXiv - MATH - Logic","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Transfer principles for forking and dividing in expansions of pure short exact sequences of Abelian groups\",\"authors\":\"Akash Hossain\",\"doi\":\"arxiv-2409.10148\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In their article about distality in valued fields, Aschenbrenner, Chernikov,\\nGehret and Ziegler proved resplendent Ax-Kochen-Ershov principles for\\nquantifier elimination in pure short exact sequences of Abelian structures. We\\nstudy how their work relates to forking, and we prove Ax-Kochen-Ershov\\nprinciples for forking and dividing in this setting.\",\"PeriodicalId\":501306,\"journal\":{\"name\":\"arXiv - MATH - Logic\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-16\",\"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-2409.10148\",\"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-2409.10148","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Transfer principles for forking and dividing in expansions of pure short exact sequences of Abelian groups
In their article about distality in valued fields, Aschenbrenner, Chernikov,
Gehret and Ziegler proved resplendent Ax-Kochen-Ershov principles for
quantifier elimination in pure short exact sequences of Abelian structures. We
study how their work relates to forking, and we prove Ax-Kochen-Ershov
principles for forking and dividing in this setting.
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