Answer by Joel David Hamkins for Undefinable inner model
This phenomenon occurs whenever there is a transitive model of ZFC.Suppose that $M$ is a countable transitive model of ZFC. Let $\newcommand\P{\mathbb{P}}\P$ be the Easton-support class product...
View ArticleAnswer by Farmer S for Undefinable inner model
Here is an example from a transitive set model of ZFC +"there is a proper class of measurable cardinals". If there is one, then there is a countable one $N$, so fix such an $N$. Fix a sequence...
View ArticleUndefinable inner model
What are some examples of a pair $M\subseteq N$ of transitive set models of $\mathsf{ZFC}$ with the same ordinals, such that $M$ is not a definable class (with parameters) in $N$? Is it possible that...
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