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

*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