@JadeVanadium: Hey there! Good to see you again!

@user21820 Oh hello :)

Hey! =)

@JadeVanadium Somehow, I always see your message a little late.. even though I am online on SE..

XD

Ah it happens to me sometimes too

I'm just too stealthy.

LOL.

It's hard to find V.

=D

:3

V is so huge. I love her

I couldn't give up a good pun.

Sorry I cannot visualize V.

=P

Anyway I need to go for a while.

np, see you later

I'm done with the while but will be busy for a much longer while now. XD

@JadeVanadium: Take care and see you next time!

You too :)

By the way, just to note something about the last discussion on topology. It makes me wonder what a 1st-order axiomatization might look like, which one might reasonably believe is robust and not subject to set-theoretic opinion.

Just like ACA is a reasonable axiomatization of ℕ that captures the 2nd-order induction better than PA.

@JadeVanadium I was thinking about this kind of topology definition.

Like, maybe we could define the topology this way and if we wish we can add the "closed under countable union" property as an extra property.

But idk, maybe this is so "not useful" that it is not worth "generalizing"...

@KripkePlatek The actual definition doesn't assume countable union, and it may well be uncountable.

If you just have binary intersection and union, you get nothing more than a lattice under ⊆.