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Sniffnoy comments on Shock Level 5: Big Worlds and Modal Realism - Less Wrong
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I dont think that the multiverse of MWI can be sensibly identified with Tegmark's multiverse; if we accept the latter, the former is just one of the universes that makes it up. The multiverse of MWI is one, complete, standalone mathematical structure; it is perhaps a multiverse from our usual point of view, but from the Tegmark multiverse point of view, it should be considered as just one universe, of which we only care about a small part.
Yes. Tegmark talks about four levels of multiverses: MWI is level 3, and the mathematical universe is level 4.
Oh, hah, that was pretty silly of me. I'd forgotten that distinction.
On that note, ISTM that the "levels" don't really form a total order - rather than 0-1-2-3-4, it seems more like 0-1-2-4 and 0-3-4 with 3 incomparable to 1 and 2.
Yeah, Tegmark says that level 3 doesn't give you anything bigger than 1 and 2 together do.