# Talk:Reflecting ordinal

From Cantor's Attic

## Reflecting a conjunctand down

A property that seems important about reflection is that for any $\Pi_n$-definable class $X$, being $\Pi_n$-reflection on Ord and in $X$ implies being $\Pi_n$-reflecting on $X$. For example, if an ordinal is $\Pi_2$-reflecting and a limit of admissibles, it's also $\Pi_2$-reflecting on the class of limits of admissibles. But I don't know how to add this to the article, since although I've seen a proof I've never seen a published proof C7X (talk) 22:10, 30 May 2022 (PDT)

- I added my own argumentation about uncountable transitive models, so if you know a proof, writing it is better than what I did. BartekChom (talk) 11:06, 3 June 2022 (PDT)
- I don't understand forcing, so about the first paragraph, this is an interesting argument and it seems like good enough explanation for this page. I've never seen a proof of this argument in literature before, so I can't cite anything, and also I'm not sure what it has to do with reflecting conjunctands down, but it seems good C7X (talk) 13:13, 4 June 2022 (PDT)