# zbMATH — the first resource for mathematics

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
Full Text: