Cofinality: Difference between revisions
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RhubarbJayde (talk | contribs) (Created page with "The cofinality of an ordinal \(\alpha\), denoted \(\mathrm{cof}(\alpha)\) or \(\mathrm{cf}(\alpha)\), is the least \(\mu\) so that there is some function \(f: \mu \to \alpha\) with unbounded range. For example: * The cofinality of \(0\) is \(0\). * The cofinality of any successor ordinal is \(1\), because the map \(f: 1 \to \alpha+1\) defined by \(f(0) = \alpha\) has unbounded range. * The cofinality of any limit of ordinal is at least \(\omega\): if it's countabl...") |
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Cofinality is used in the definition of [[Inaccessible cardinal|weakly inaccessible]] cardinals.
==Without choice==
Citation about every uncountable cardinal being singular being consistent with ZF
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