- #1
tzimie
- 259
- 28
I am fascinated by the Fast growing hierarchy. Up to epsilon-naught, and even above, in Veblen hierarchy any value, say, Veblen function Fi(1000, 3) can be theoretically expanded into a very long string of function calls, ultimately repeating the successor function (f0). Anyway these ordinals are countable, and for the finite input we get huge but finite output.
What I don't understand is beyond Veblen: https://en.wikipedia.org/wiki/Ordinal_collapsing_function
The point where I am lost is when the uncountable Omega is injected out of the blue. I don't understand if it is possible, from that point on, to expand the functions indexed with such ordinals with finite input into finite strings. May be this is because I don't understand why the injection of uncountable ordinal does not make the whole structure uncountable.
Please unstuck me, looks like I've just reached the fixed point of my brain )
What I don't understand is beyond Veblen: https://en.wikipedia.org/wiki/Ordinal_collapsing_function
The point where I am lost is when the uncountable Omega is injected out of the blue. I don't understand if it is possible, from that point on, to expand the functions indexed with such ordinals with finite input into finite strings. May be this is because I don't understand why the injection of uncountable ordinal does not make the whole structure uncountable.
Please unstuck me, looks like I've just reached the fixed point of my brain )