{"title":"Preservation of Topological Properties by Strongly Proper Forcings","authors":"Thomas Gilton, Jared Holshouser","doi":"arxiv-2408.02495","DOIUrl":null,"url":null,"abstract":"In this paper we show that forcings which are strongly proper for\nstationarily many countable elementary submodels preserve each of the following\nproperties of topological spaces: countably tight; Lindel\\\"of; Rothberger;\nMenger; and a strategic version of Rothberger. This extends results from Dow,\nas well as from Iwasa and from Kada.","PeriodicalId":501306,"journal":{"name":"arXiv - MATH - Logic","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-05","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-2408.02495","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 this paper we show that forcings which are strongly proper for
stationarily many countable elementary submodels preserve each of the following
properties of topological spaces: countably tight; Lindel\"of; Rothberger;
Menger; and a strategic version of Rothberger. This extends results from Dow,
as well as from Iwasa and from Kada.
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