{"title":"ARTIN–SCHREIER EXTENSIONS AND COMBINATORIAL COMPLEXITY IN HENSELIAN VALUED FIELDS","authors":"BLAISE BOISSONNEAU","doi":"10.1017/jsl.2024.34","DOIUrl":null,"url":null,"abstract":"<p>We give explicit formulas witnessing IP, IP<span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240911114232841-0471:S0022481224000343:S0022481224000343_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$_{\\!n}$</span></span></img></span></span>, or TP2 in fields with Artin–Schreier extensions. We use them to control <span>p</span>-extensions of mixed characteristic henselian valued fields, allowing us most notably to generalize to the NIP<span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240911114232841-0471:S0022481224000343:S0022481224000343_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$_{\\!n}$</span></span></img></span></span> context one way of Anscombe–Jahnke’s classification of NIP henselian valued fields. As a corollary, we obtain that NIP<span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240911114232841-0471:S0022481224000343:S0022481224000343_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$_{\\!n}$</span></span></img></span></span> henselian valued fields with NIP residue field are NIP. We also discuss tameness results for NTP2 henselian valued fields.</p>","PeriodicalId":501300,"journal":{"name":"The Journal of Symbolic Logic","volume":"16 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Journal of Symbolic Logic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/jsl.2024.34","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 give explicit formulas witnessing IP, IP$_{\!n}$, or TP2 in fields with Artin–Schreier extensions. We use them to control p-extensions of mixed characteristic henselian valued fields, allowing us most notably to generalize to the NIP$_{\!n}$ context one way of Anscombe–Jahnke’s classification of NIP henselian valued fields. As a corollary, we obtain that NIP$_{\!n}$ henselian valued fields with NIP residue field are NIP. We also discuss tameness results for NTP2 henselian valued fields.
$_{\!n}$, or TP2 in fields with Artin–Schreier extensions. We use them to control p-extensions of mixed characteristic henselian valued fields, allowing us most notably to generalize to the NIP
$_{\!n}$ context one way of Anscombe–Jahnke’s classification of NIP henselian valued fields. As a corollary, we obtain that NIP
$_{\!n}$ henselian valued fields with NIP residue field are NIP. We also discuss tameness results for NTP2 henselian valued fields.
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
