{"title":"在谢拉无处密集超滤波器模型中添加超滤波器","authors":"Dilip Raghavan, Juris Stepr\\= ans","doi":"arxiv-2408.04446","DOIUrl":null,"url":null,"abstract":"We exhibit a forcing for producing a model with no nowhere dense ultrafilters\nthat satisfies the full Sacks Property. By interleaving this forcing with other\nforcing notions, a model containing a $(2, {\\aleph}_{0})$-selective\nultrafilter, but no nowhere dense ultrafilters is produced. It is thus proved\nthat the existence of $(2, {\\aleph}_{0})$-selective ultrafilters does not imply\nthe existence of nowhere dense ultrafilters.","PeriodicalId":501306,"journal":{"name":"arXiv - MATH - Logic","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Adding ultrafilters to Shelah's model for no nowhere dense ultrafilters\",\"authors\":\"Dilip Raghavan, Juris Stepr\\\\= ans\",\"doi\":\"arxiv-2408.04446\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We exhibit a forcing for producing a model with no nowhere dense ultrafilters\\nthat satisfies the full Sacks Property. By interleaving this forcing with other\\nforcing notions, a model containing a $(2, {\\\\aleph}_{0})$-selective\\nultrafilter, but no nowhere dense ultrafilters is produced. It is thus proved\\nthat the existence of $(2, {\\\\aleph}_{0})$-selective ultrafilters does not imply\\nthe existence of nowhere dense ultrafilters.\",\"PeriodicalId\":501306,\"journal\":{\"name\":\"arXiv - MATH - Logic\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-08\",\"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-2408.04446\",\"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-2408.04446","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Adding ultrafilters to Shelah's model for no nowhere dense ultrafilters
We exhibit a forcing for producing a model with no nowhere dense ultrafilters
that satisfies the full Sacks Property. By interleaving this forcing with other
forcing notions, a model containing a $(2, {\aleph}_{0})$-selective
ultrafilter, but no nowhere dense ultrafilters is produced. It is thus proved
that the existence of $(2, {\aleph}_{0})$-selective ultrafilters does not imply
the existence of nowhere dense ultrafilters.