# Talk:Constructible universe

## Relativized constructible universe facts

Posting this here since trying to put it on the article gives me a 500 error

For an ordinal $\alpha$ and a class ([1]) $u$, the following two conditions are equivalent:

• There is a $\Sigma_1$-definable $a\subset u$ such that $a\notin L_\alpha[u]$. (What if Jensen uses a different definition of "$L_\alpha[u]$"?)
• There is a $\Sigma_1$-definable map from a subset of $u$ onto $L_\alpha[u]$.

For an ordinal $\alpha$ and a set $u$, the following two conditions are equivalent:

• There is a $\Delta_1$-definable $a\subset u$ such that $a\notin L_\alpha[u]$.
• There is a $\Delta_1$-definable map from a subset of $u$ onto $L_\alpha[u]$. Typos here, the article has an updated version

Source: [2] (pp. 14-16) C7X (talk) 14:18, 14 August 2021 (PDT)

I managed to insert your facts. It seems that the bugs block mainly sending parentheses after TeX. You can try previewing with only the beginning of the section (temporarily removing the rest) to localise bad places. BartekChom (talk) 22:28, 14 August 2021 (PDT)
Thanks. Jensen's definition $L_\alpha[u]$ looks like it matches this article's convention too C7X (talk) 22:41, 14 August 2021 (PDT)