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Regular cardinals in models of ZF. (English) Zbl 0589.03033
Summary: We prove the following Theorem: Suppose M is a countable model of ZFC and \(\kappa\) is an almost huge cardinal in M. Let A be a subset of \(\kappa\) consisting of nonlimit ordinals. Then there is a model \(N_ A\) of ZF such that \(\aleph_{\alpha}\) is a regular cardinal in \(N_ A\) iff \(\alpha\in A\) for every \(\alpha >0\).

MSC:
03E55 Large cardinals
03C62 Models of arithmetic and set theory
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