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Question about a Ramsey graph.

  1. Dec 30, 2012 #1
    the Ramsey number of [itex] R(\omega,\omega)=\omega [/itex]
    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 cant
    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.
  2. jcsd
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