very cultured, nice

bless. this is the best stuff on my skyline rn 🫡

like you can take a look at the wacky stuff here, it's not hard to e.g. describe ordinals so large ZFC can't construct them, or any other particular computable list of axioms for set theory! https://en.wikipedia.org/wiki/Large_countable_ordinal

*how weird definite-but-not-surveyable collections are like the collection of countable ordinals is truly insanely large, almost all of them are impossible to describe in any fixed ordinal notation, e.g. almost all of them are uncomputable. it's extremely different in character from N

i haven't thought through this carefully but yeah, i think in this framework aleph_1, or more precisely omega_1 thought of as the collection of all countable ordinals, is definite but not surveyable. in other papers i think he does a good job emphasizing how weird surveyable collections are

just got on here to quickly scope out the vibes! looks like they're p good

🥳

i admire your bravery

naturally 🥲

🫡🙏