- #1

cragar

- 2,552

- 3

but then [itex] R(\omega+1,\omega)=\omega_1 [/itex]

My question is on the second one can we do a counter example to show that it can't

be any countable ordinal.

depending on how I count the natural numbers I can get any countable ordinal I want.

If we assume that [itex] R(\omega+1,\omega) [/itex] was equal to some countable ordinal

then I could just color [itex] \omega [/itex] edges with blue for example and i would stay

under the [itex] \omega+1 [/itex] limit . And the other color we would just use a finite number of them.

I guess i don't really understand why order matters for an infinite Ramsey graph.

It doesn't seem like it matters in the finite case.