Where does this number appear in public?
Nowhere I assume. Just like a few others mentioned on this thread. I just wanted to give the people who actually know what they are talking about something somewhat harder than 6 or 1000 to beat. I knew they could easily do that.
COCN
=
f
ψ
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Ω
Ω
Ω
⋯
)
(
f
ψ
(
Ω
Ω
Ω
⋯
)
(
f
ψ
(
Ω
Ω
Ω
⋯
)
(
1000
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)
And also, I'm the first one who's ever mentioned this number. I literally invented this number just for this forum
(also, you don’t have to delete your posts, you can simply edit them)
Also I’m the first one who’s ever mentioned this number
Alright, but what is the number…?
What does your notation mean?
This is a function within the fast growing hierarchy. Using the and the an expansion of the bachman howard ordinal as The ordinal is notated by:
ψ
(
Ω
Ω
Ω
⋯
)
They’re supposed to be under each other. But I can’t write a perfect HTML code. And I applied that Ordinal into the fast growing hierarchy for
f
ψ
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Ω
Ω
Ω
⋯
)
Then I applied that function to itself three times
I’m sorry, but I cannot make soup from this…
You mean ΩΩΩ…? How is this defined?
I’ve seen Ω referring to the least uncountable ordinal, but a tower of subscripts does not make sense to me with that interpretation.
Do you mean ε0=ω^ω^ω^…? Or do you mean the least fixed point for the aleph numbers?
The least uncountable ordinal in this case is w_1 (w is omega I don’t have a lot to work with here)
Ω
1
In this case is. w_2
Ω
2
= w_3
Ω
Ω
= w_w1
Do you kind of get the picture now?
I looked up the Bachmann-Howard ordinal, and Wikipedia says it is a large countable ordinal, but then defines it in a way that is clearly greater than $\Omega$, the least uncountable ordinal… one of the editors was confused
I wish for latex on these forums
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It goes that way enough, it would be handy 
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LaTeX should be in every forum
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I found the page on ordinal collapsing functions helpful reading, although I’m still in the process of understanding what the Bachmann-Howard ordinal is (and sadly don’t have too much time)…
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That page was helpful. I was the one who was confused - you can generate uncountable ordinals with $\Omega$, but as long as there is a countable ordinal that is not generated, $\varphi$ will take a countable value.
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I was just about to post that video and name-drop the Hyper Moser 
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I’m still trying to wrap my head around Bachman-Howard.
The uncountable cardinal is used to be able to define new countable ordinals, since we have a way to talk about something “a lot larger”.
However, I don’t see why taking a far larger uncountable cardinal that still does not have any large cardinal properties would allow us to express new concepts that we couldn’t have already expressed with smaller cardinals… Doesn’t the psi function stabilise?
Its true that psi function stabilising at some point, but when we introduce a new, much larger uncountable cardinal (even without large cardinal properties), it allows psi to define new countable ordinals that were previously inaccessible. Just try to put it like this:
Imagine you’re building ordinals step by step. If you only have small cardinals, there’s a limit to how far you can go before the psi function stops producing new ordinals, howewer
by bringing in a significantly larger uncountable cardinal, you create a “jump” in the hierarchy, which allows psi to construct new countable ordinals that were impossible to reach before.
So yes, psi functios stabilising, but not globaly. It stabilizes to a given setup, but by increasing it, we extend what can be defined
P.S sorry if I’m bad at explaning or I mistaken at some point, but I tried to give my best 