user820789

my thinking / understanding is as follows: in the og veblen there is no way to write the LVO (please correct me if im wrong). so in my notation, that would be the point you switch to φ''(0)

"here's a completely differently structured kind of ordinal collapsing function that behaves more like the Veblen function " which?

@SimplyBeautifulArt do you have any references or futher explanation of "Namely, instead of just a map from indices to parameters you have a map from indices to maps!"?

"If you want to convey your ideas to others, you should learn to precisely express them." is me right now

@SimplyBeautifulArt made another attempt at cleaning up the notation. i would add definitions, but i'm not really sure how (i'm such a noob #facepalm)

@SimplyBeautifulArt made an update to my MO post. hopefully it is more clear.

alright. thanks again-

my idea was to create a veblen esque structure where the 1st tier is the original veblen function

one quick(?) question before i go: what do you make of the xi function from my post?

i gotta run for now. thanks again for taking the time to chat! i might ping you again sometime if i can get my thoughts sorted-

no worries.

it also might not!

maybe this question i asked might give some insight into how im approaching things: math.stackexchange.com/questions/3006787/…

deriving fundamental sequences from closures is something im going to look into more

so epsilon is the epsilon-th oridnal closed under addition?

$\phi_0(\varepsilon_0)=\phi_1(0)$ ?

what about epsilon?

more or less

i wish i had a better grasp on veblen, ocfs, ordinals & cardinals so i could more concisely communicate my thinking

you mentioned listing fundamental sequences is not the right strategy for things like w_1 & k

ok, i'm most familiar with the veblen function, so perhaps we can talk more in that context. what i'm struggling with is how to swap between the og version & modifications. do i just magically pull things like w_1 or k (an inaccessible) out of a hat or ??

quick aside: how familiar are you with surreal numbers?

i have mostly seen ocfs that use w_1 - which i presume these will cap out before w_1. i just started seeing ocfs with inaccessibles recently. but i presume these will cap out before inaccessibles. is that correct?

sounds simple enough

i'm not familiar with stationary points

ok..

what about omega_1?

how would i write out what omega is the closure of?

ok, i have seen that before

i'm curious if you could tell me more about closure. it seems like a useful shift in thinking when moving higher up the transfinite hierarchy

i've seen so many i can't even reference which ones i like

2ndly, thanks for all the amazing answers you post!

1st of all, thanks for taking the time to chat with me!

@SimplyBeautifulArt hey!

@SimplyBeautifulArt did you create the $\omega_\star$ notation here (math.stackexchange.com/questions/83204/…)? or did u get it from somwhere?

@MarkS.

i understand that u dont understand that

i am above average

i think it's a good thing that i am not fairly good or average

@MarkS.

sparknotes.com/lit/godot/summary

got some work on my book done

i understand; im not, however, reasonable (fairly good; average)

foundations, foundations, foundations!

also, i will continue to repeat that i understand ur perspective

re: idempotents, i meant games like far star

@MarkS. foundations looks great! understood as well re: order of operations (proofs, graph/set theory, transfinite non-loopy + finite loopy games.

1 question i have regards $\frac{\omega}{\omega}$: is it's birthday $\omega^2$? (using the logic that frac{omega}{2} is born on day 2\omega) or 2\omega (using the logic the frac{2}{omega} is born on day \omega+1) ?

if i am understanding correctly: $\frac{\omega}{2}$ is born on day $2\omega$ (as is w^-2)