{"title":"Tameness Properties in Multiplicative Valued Difference Fields with Lift and Section","authors":"Christoph Kesting","doi":"arxiv-2409.10406","DOIUrl":null,"url":null,"abstract":"We prove relative quantifier elimination for Pal's multiplicative valued\ndifference fields with an added lifting map of the residue field. Furthermore,\nwe generalize a $\\mathrm{NIP}$ transfer result for valued fields by Jahnke and\nSimon to $\\mathrm{NTP}_2$ to show that said valued difference fields are\n$\\mathrm{NTP}_2$ if and only if value group and residue field are.","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-2409.10406","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 prove relative quantifier elimination for Pal's multiplicative valued
difference fields with an added lifting map of the residue field. Furthermore,
we generalize a $\mathrm{NIP}$ transfer result for valued fields by Jahnke and
Simon to $\mathrm{NTP}_2$ to show that said valued difference fields are
$\mathrm{NTP}_2$ if and only if value group and residue field are.
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