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$\begingroup$ Wouldn't it be Woodinness? :) $\endgroup$
– Mariano Suárez-Álvarez
Commented May 3, 2011 at 1:12
$\begingroup$ I knew there was something weird in that paragraph. But I was worried about whether to write "strength" or "strongness" (as Joel does), and ended up using neither and not fixing the typo. Thanks! $\endgroup$
– Andrés E. Caicedo
Commented May 3, 2011 at 1:22
$\begingroup$ Thanks to you all for your very illuminating answers. Even though the relative size of the cardinals involved seems not to be a good way of ranking these axioms, it appears to me that the more we know about these relative sizes, the sharper becomes our intuitive picture of the universe (or the "possible universes") of set theory. $\endgroup$
– Garabed Gulbenkian
Commented May 3, 2011 at 17:20
$\begingroup$ Oh, sure, I agree. And even on a purely pragmatic level, it is important to study both orderings, to be aware that they differ. $\endgroup$
– Andrés E. Caicedo
Commented May 3, 2011 at 17:24

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