{"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":"7 1","pages":""},"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}
引用次数: 0
Abstract
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.