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Results tagged with inner-models
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user 479330
An inner model is a transitive proper class substructure of the universe of sets, that satisfies $\mathsf{ZF}(\mathsf{C})$.
5
votes
Do all limit $\alpha \in \omega_1^L$ satisfy $L_\alpha \models V=HC$?
As Asaf mentioned, this is not true. It's indeed true that when $\alpha$ is a gap ordinal $L_\alpha\vDash\textrm{V=HC}$, but when considering some ordinals above gap ordinals we get points where it fa …
- 2,031
1
vote
Why can't $L_\beta$ contain a real coding a well-ordering of order-type $\beta$, when $\beta...
A proof now appears as lemma 1.21 of the poster's bachelor's thesis "The real numbers in inner models of set theory" (2022, arXiv), however I have a doubt about the proof which is expressed in a comme …
- 2,031