Answer by Farmer S for Minimum transitive models and V=L
Yes, I claim you can in fact get one whose minimum model is a set forcing extension of a segment of $L$. Let $L_\alpha$ be least modelling ZFC. Let $\mathbb{P}=\mathbb{P}^{L_\alpha}$ be Jensen's...
View ArticleAnswer by Ali Enayat for Minimum transitive models and V=L
Here is another partial result; it complements Joel Hamkins' answer. Note that in the following theorem, $T$ is not necessarily a c.e. theory.Theorem.Suppose$T$is an extension of$\mathrm{ZF} + \exists...
View ArticleAnswer by Joel David Hamkins for Minimum transitive models and V=L
This is not a full answer, but I found it interesting to notice that if we relax the c.e. requirement somewhat, then there is a sweeping positive answer.Theorem. Every complete theory extending ZFC +...
View ArticleMinimum transitive models and V=L
Is there a c.e. theory $T⊢\text{ZFC}$ in the language of set theory such that the minimum transitive model of $T$ exists but does not satisfy $V=L$?You may assume that ZFC has transitive models. Note...
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