Yes, its omega times 3, and it’s not 3 times omega. You can read about ordinal multiplication here.

]]>Yes!

]]>After a while we reach

should read

]]>But since you had such fun with ordinals here (and here and here), I better add that Ketonen and Solovay later gave a proof based on the ε_{0} stuff and the hierarchy of fast-growing functions. (The variation due to Loebl and Nešetřil is nice and short.) We should talk about this sometime! I wish I understood all the connections better. (Stillwell’s Roads to Infinity offers a nice entry point, though he does like to gloss over details.)

Alas, I haven’t thought about ordinal tetration for a long time, so I couldn’t say anything interesting without some time to review what I once knew!

]]>Here is some quite interesting discussion. Would you care to comment on it?

]]>Thanks for catching that! Fixed.

]]>The main surprise is that ordinal addition is not commutative. We’ve seen that , since

Note the missing in the definition of .

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