{"title":"无\\ aleph_k美元热电联供装置","authors":"M. Dugas, D. Herden, S. Shelah","doi":"10.4171/rsmup/58","DOIUrl":null,"url":null,"abstract":"We prove in ZFC that an abelian group $C$ is cotorsion if and only if $\\operatorname{Ext}(F,C) = 0$ for every $\\aleph_k$-free group $F$, and discuss some consequences and related results. This short note includes a condensed overview of the $\\bar\\lambda$-Black Box for $\\aleph_k$-free constructions in ZFC.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"7 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"$\\\\aleph_k$-free cogenerators\",\"authors\":\"M. Dugas, D. Herden, S. Shelah\",\"doi\":\"10.4171/rsmup/58\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove in ZFC that an abelian group $C$ is cotorsion if and only if $\\\\operatorname{Ext}(F,C) = 0$ for every $\\\\aleph_k$-free group $F$, and discuss some consequences and related results. This short note includes a condensed overview of the $\\\\bar\\\\lambda$-Black Box for $\\\\aleph_k$-free constructions in ZFC.\",\"PeriodicalId\":20997,\"journal\":{\"name\":\"Rendiconti del Seminario Matematico della Università di Padova\",\"volume\":\"7 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-09-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Rendiconti del Seminario Matematico della Università di Padova\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4171/rsmup/58\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Rendiconti del Seminario Matematico della Università di Padova","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/rsmup/58","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We prove in ZFC that an abelian group $C$ is cotorsion if and only if $\operatorname{Ext}(F,C) = 0$ for every $\aleph_k$-free group $F$, and discuss some consequences and related results. This short note includes a condensed overview of the $\bar\lambda$-Black Box for $\aleph_k$-free constructions in ZFC.
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