Timeline for Is it consistent that the gaps between cardinals $\kappa$ and $2^\kappa$ "get larger and larger"?
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| May 10, 2016 at 12:00 | comment | added | Gro-Tsen | @DominicvanderZypen Now this, unlike your original question, is reducible to Easton's theorem, which is a much easier result than Foreman-Woodin. Basically, you can make $2^{\aleph_0}$ equal to whatever $\kappa$ you like provided only that it has uncountable cofinality. (In particular, of $\kappa$ is the smallest fixed point of uncountable cofinality of $\alpha\mapsto\omega_\alpha$, you can make $2^{\aleph_0}=\kappa$.) | |
| May 10, 2016 at 11:47 | comment | added | Dominic van der Zypen | Thanks for this link! So if I understand it correctly, as a special case, given an ordinal $\beta$, it is consistent that $2^{\aleph_0} \geq \aleph_\beta$? Is it also possible that $2^{\aleph_0} = \aleph_{2^{\aleph_0}}$? (The answer to the latter is perhaps "No", for some simple reason that escapes me at the moment.) | |
| May 10, 2016 at 11:30 | vote | accept | Dominic van der Zypen | ||
| May 10, 2016 at 11:28 | history | answered | Mohammad Golshani | CC BY-SA 3.0 |