Answer by Monroe Eskew for Kunen's use of Countable Transitive Models
If there is any ordinal $\alpha$ such that $L_\alpha$ satisfies ZFC, then consider the least one. This is some countable ordinal $\beta$. It is easy to show that $L_\beta \vDash$ "There is no...
View ArticleAnswer by Jason for Kunen's use of Countable Transitive Models
Here are some examples that might help in understanding. If ZFC is consistent, then it follows we have a set model $M$ of the theory. Consider a nonprincipal ultrafilter $U$ on $\omega$ and let...
View ArticleAnswer by Stefan Hoffelner for Kunen's use of Countable Transitive Models
It is true that you can use Löwenheim Skolem to get a countable model $M$ of ZFC assuming $Con(ZFC)$. But to use Mostowski you need additionally the well foundedness of that model, which doesn't have...
View ArticleKunen's use of Countable Transitive Models
Hi, I have a doubt concerning Kunen's exposition of forcing in his classical book (arguably $the$ book on forcing). When dealing with Countable Transitive Models to set up the forcing machinery, Kunen...
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