{"title":"Generating some large filters of quasiorder lattices","authors":"Gábor Czédli","doi":"10.1007/s44146-024-00139-5","DOIUrl":null,"url":null,"abstract":"<div><p>For a poset <span>\\((P;\\le )\\)</span>, the quasiorders (AKA preorders) extending the poset order “<span>\\(\\le \\)</span>” form a complete lattice <i>F</i>, which is a filter in the lattice of all quasiorders of the set <i>P</i>. We prove that if the poset order “<span>\\(\\le \\)</span>” is small, then <i>F</i> can be generated by few elements.</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"91 1-2","pages":"1 - 21"},"PeriodicalIF":0.6000,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACTA SCIENTIARUM MATHEMATICARUM","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s44146-024-00139-5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
For a poset \((P;\le )\), the quasiorders (AKA preorders) extending the poset order “\(\le \)” form a complete lattice F, which is a filter in the lattice of all quasiorders of the set P. We prove that if the poset order “\(\le \)” is small, then F can be generated by few elements.