Description:
Form 40 does not imply Form 44
Content:
Form 40 does not imply Form 44 by the following theorem which is proved in Jech [1966b]}:
Let \(M\) be a countable standard model for \(ZF +AC\) and \(\alpha\) a regular, infinite cardinal in \(M\). Then there is a model \(N\) of \(ZF\) containing \(M\) with the same ordinals as \(M\) such that in \(N\), \(\neg DC(\alpha)\) (see Form 87), \(\neg C(\alpha ,2)\) and there is a cardinal incomparable with \(\alpha\). But for every \(\beta < \alpha\), \(DC(\beta)\) and \(C(\beta,\infty)\) hold and \(\beta\) is comparable with every cardinal.
Howard-Rubin number:
14
Type:
Inequivalency
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