{"title":"增加亚伯拉罕俱乐部和α$正确性","authors":"Mohammad Golshani, Rouholah Hoseini Naveh","doi":"arxiv-2409.09697","DOIUrl":null,"url":null,"abstract":"For every indecomposable ordinal $\\alpha < \\omega_1$, we introduce a variant\nof Abraham forcing for adding a club in $\\omega_1$, which is $<\\alpha$-proper\nbut not $\\alpha$-proper.","PeriodicalId":501306,"journal":{"name":"arXiv - MATH - Logic","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Adding Abraham clubs and $α$-properness\",\"authors\":\"Mohammad Golshani, Rouholah Hoseini Naveh\",\"doi\":\"arxiv-2409.09697\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For every indecomposable ordinal $\\\\alpha < \\\\omega_1$, we introduce a variant\\nof Abraham forcing for adding a club in $\\\\omega_1$, which is $<\\\\alpha$-proper\\nbut not $\\\\alpha$-proper.\",\"PeriodicalId\":501306,\"journal\":{\"name\":\"arXiv - MATH - Logic\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-15\",\"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-2409.09697\",\"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-2409.09697","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
For every indecomposable ordinal $\alpha < \omega_1$, we introduce a variant
of Abraham forcing for adding a club in $\omega_1$, which is $<\alpha$-proper
but not $\alpha$-proper.
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