{"title":"关于难波强迫和最小坍塌","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":"{\"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}","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}
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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