{"title":"Geometric Condition For Dependent Choice","authors":"A. Karagila, J. Schilhan","doi":"10.1007/s10474-024-01396-0","DOIUrl":null,"url":null,"abstract":"<p>We provide a geometric condition which characterises when the\nPrinciple of Dependent Choice holds in a Fraenkel-Mostowski-Specker permutation\nmodel. This condition is a slight weakening of requiring the filter of groups to\nbe closed under countable intersections. We show that this condition holds nontrivially\nin a new permutation model we call \"the nowhere dense model\" and we\nstudy its extensions to uncountable cardinals as well.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Hungarica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10474-024-01396-0","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We provide a geometric condition which characterises when the
Principle of Dependent Choice holds in a Fraenkel-Mostowski-Specker permutation
model. This condition is a slight weakening of requiring the filter of groups to
be closed under countable intersections. We show that this condition holds nontrivially
in a new permutation model we call "the nowhere dense model" and we
study its extensions to uncountable cardinals as well.
期刊介绍：
Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.
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