{"title":"On Namba Forcing and Minimal Collapses","authors":"Maxwell Levine","doi":"arxiv-2408.03487","DOIUrl":null,"url":null,"abstract":"We build on a 1990 paper of Bukovsky and Coplakova-Hartova. First, we remove\nthe hypothesis of $\\textsf{CH}$ from one of their minimality results. Then,\nusing a measurable cardinal, we show that there is a\n$|\\aleph_2^V|=\\aleph_1$-minimal extension that is not a\n$|\\aleph_3^V|=\\aleph_1$-extension, answering the first of their questions.","PeriodicalId":501306,"journal":{"name":"arXiv - MATH - Logic","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-07","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-2408.03487","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 build on a 1990 paper of Bukovsky and Coplakova-Hartova. First, we remove
the hypothesis of $\textsf{CH}$ from one of their minimality results. Then,
using a measurable cardinal, we show that there is a
$|\aleph_2^V|=\aleph_1$-minimal extension that is not a
$|\aleph_3^V|=\aleph_1$-extension, answering the first of their questions.
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