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Nov 19, 2014 at 0:15 comment added Joel David Hamkins Thanks very much, Noah, this is great. Would it be possible for you to elaborate a little more on the EF game analysis?
Nov 18, 2014 at 21:39 comment added François G. Dorais I was still editing it, you beat me to the punchline.
Nov 18, 2014 at 21:37 comment added Noah Schweber @FrançoisG.Dorais, somehow I missed your answer when I was writing mine.
Nov 18, 2014 at 21:15 comment added François G. Dorais I think $\omega^\omega$ is enough but, as I explain in my answer, I only sketched the calculations.
Nov 18, 2014 at 21:08 comment added Noah Schweber Actually, I think we just need to go up to rank, say, $\epsilon_0$ (again, I'm sure I'm overshooting) and have infinitely many children of each lower rank.
Nov 18, 2014 at 21:05 history answered Noah Schweber CC BY-SA 3.0