Is there a model of ${\sf (ZFC)}$ such that in the model we have that $\kappa$ is a limit cardinal if and only if $2^\kappa$ is a limit cardinal?
$\begingroup$
$\endgroup$
5
asked Jan 23, 2019 at 15:46
-
6$\begingroup$ A related question: mathoverflow.net/questions/226887/… $\endgroup$– Will BrianJan 23, 2019 at 16:00
-
6$\begingroup$ Actually, this comment to the answer is exactly the present question. $\endgroup$– Pedro Sánchez TerrafJan 23, 2019 at 16:18
-
6$\begingroup$ This is definitely not an easy question - indeed, a model like this would violate the singular cardinal hypothesis, and negation of SCH has quite high consistency strength. $\endgroup$– WojowuJan 23, 2019 at 16:29
-
$\begingroup$ @Wojowu "definitely not easy" if the answer is "yes". But it is conceivable that there is an easy "no"... $\endgroup$– GoldsternJan 26, 2019 at 9:25
-
$\begingroup$ @Goldstern I wouldn't expect an easy "no" either personally, seeing how difficult it is to study the continuum function at singular cardinals whatsoever (and also because I would expect the answer to be yes :P ) $\endgroup$– WojowuJan 26, 2019 at 9:46
Add a comment
|