What mean $L(\mathbb{R})$ and $L(\mathbb{R})^*$?

Question

I found them relating a cardinality question here.

Does it have anything to do with regularity/computability?

@AndrésCaicedo should be able to answer, since this question directly concerns a comment by him. — Alex M., Apr 14 '16 at 10:42
It is not an abandoned question. I am still waiting an answer and I am ready to accept/upvote it. — peterh, Jul 30 '16 at 12:15
@AsafKaragila I flagged for a mod to search in the deleted comments, but it didn't exist. I can't remember, where is it from, but I am 99% sure, it is from a reasonable source. — peterh, Aug 07 '17 at 20:36
Maybe you mean $L(\Bbb R^*)$, which has meaning in the context of models of AD? — Asaf Karagila, Aug 07 '17 at 20:50
@AsafKaragila Likely this was what I've seen. Thanks - these infos are already enough to learn after it. — peterh, Aug 10 '17 at 08:23

score 3 · Accepted Answer · answered Aug 07 '17 at 00:05

$L(\mathbb{R})$ is the the constructible universe built over $\mathbb{R}$ (i.e. we can use the "real" reals as parameters). Here is the wiki page and here is some information on its construction (beginning on page 3 ~ relative construction). I have never seen $L(\mathbb{R})^*$ before, it also does not appear on the page you have linked to. Then again, I am not a set theorist.

What mean $L(\mathbb{R})$ and $L(\mathbb{R})^*$?

1 Answers1