Giorgio Laguzzi, Heike Mildenberger, Brendan Stuber-Rousselle
{"title":"On splitting trees","authors":"Giorgio Laguzzi, Heike Mildenberger, Brendan Stuber-Rousselle","doi":"10.1002/malq.202200022","DOIUrl":null,"url":null,"abstract":"<p>We investigate two variants of splitting tree forcing, their ideals and regularity properties. We prove connections with other well-known notions, such as Lebesgue measurablility, Baire- and Doughnut-property and the Marczewski field. Moreover, we prove that any <i>absolute</i> amoeba forcing for splitting trees necessarily adds a dominating real, providing more support to Hein's and Spinas' conjecture that <math>\n <semantics>\n <mrow>\n <mo>add</mo>\n <mo>(</mo>\n <msub>\n <mi>I</mi>\n <mi>SP</mi>\n </msub>\n <mo>)</mo>\n <mo>≤</mo>\n <mi>b</mi>\n </mrow>\n <annotation>$\\operatorname{add}(\\mathcal {I}_\\mathbb {SP}) \\le \\mathfrak {b}$</annotation>\n </semantics></math>.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/malq.202200022","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/malq.202200022","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
We investigate two variants of splitting tree forcing, their ideals and regularity properties. We prove connections with other well-known notions, such as Lebesgue measurablility, Baire- and Doughnut-property and the Marczewski field. Moreover, we prove that any absolute amoeba forcing for splitting trees necessarily adds a dominating real, providing more support to Hein's and Spinas' conjecture that .