{"title":"Analytic Hardy fields","authors":"Aschenbrenner, Matthias, Dries, Lou van den","doi":"10.48550/arxiv.2311.07352","DOIUrl":null,"url":null,"abstract":"We show that maximal analytic Hardy fields are $\\eta_1$ in the sense of Hausdorff. We also prove various embedding theorems about analytic Hardy fields. For example, the ordered differential field $\\mathbb T$ of transseries is shown to be isomorphic to an analytic Hardy field.","PeriodicalId":496270,"journal":{"name":"arXiv (Cornell University)","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv (Cornell University)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.48550/arxiv.2311.07352","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
We show that maximal analytic Hardy fields are $\eta_1$ in the sense of Hausdorff. We also prove various embedding theorems about analytic Hardy fields. For example, the ordered differential field $\mathbb T$ of transseries is shown to be isomorphic to an analytic Hardy field.
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