{"title":"解析Hardy域","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":"111 8","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":\"111 8\",\"pages\":\"0\"},\"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}","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}
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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