# Set theory without choice: not everything on cofinality is possible

Archive for Mathematical Logic 36 (2):81-125 (1997)

 Abstract .We prove in ZF+DC, e.g. that: if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\mu=|{\cal H}|$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\mu>\cf>\aleph_0$\end{document} then \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\mu ^+$\end{document} is regular but non measurable. This is in contrast with the results on measurability for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\mu=\aleph_\omega$\end{document} due to Apter and Magidor [ApMg]. Keywords Legacy Categories (categorize this paper) ISBN(s) DOI 10.1007/s001530050057 Options Edit this record Mark as duplicate Export citation Request removal from index

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## Citations of this work BETA

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