Answer by Alex Kruckman for The intersection of a class of ordinals belongs...
You need to assume $C$ is non-empty (otherwise $\bigcap C$ doesn't make sense).Since the ordinals are well-ordered, every non-empty class of ordinals has a least element. Let $\alpha$ be the least...
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I'm learning Ordinals as well. How about this for a proof. I'm assuming you have proved $\bigcap C$ is an ordinal, as you have stated.Suppose $c\in C$. Then $\bigcap C \subseteq c$. And as $c$ and...
View ArticleThe intersection of a class of ordinals belongs to the class
Let $C$ be a non-empty class of ordinals. I want to prove that $\bigcap C \in C.$ What I managed to prove so far :That $\bigcap C$ is an ordinal.If $\alpha \in C$, that $\bigcap (\alpha^+ \cap C) =...
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