As far as I know, only 4 set theory papers were published in the Annals in the 21st century (and only one in recursion theory).What do you count as set theory? 03E as primary MSC? In true obsessive EJMR spirit I did a quick search on Mathscinet, and since 2000 I found 6 in Annals, 4 in Acta, 1 in Publ. IHES and 3 in Inventiones. Also, while it's obviously very small number statistics, it seemed to me that publications in 03E (and 03 in general) seemed to be concentrated more towards the recent years.
I relied on my memory to come up with the number 4. After looking it up on the Annals' website, there seem to be 8 papers with 03E as primary. However, there should be a consensus that the Freedman paper is not considered set theory. The two circle squaring papers are also not really set theory (no forcing, inner models, large cardinals, infinite combinatorics or descriptive set theory beyond Borel sets) and are mostly labeled 03E for cultural reasons. This leaves us with 5 papers (looks like I missed one after all). Assuming that at least ~5,000 set theory papers were uploaded to arxiv in the current century, this gives a 0.1% publication rate in the Annals.
