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?
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6$\begingroup$ A related question: mathoverflow.net/questions/226887/… $\endgroup$ – Will Brian Jan 23 at 16:00

6$\begingroup$ Actually, this comment to the answer is exactly the present question. $\endgroup$ – Pedro Sánchez Terraf Jan 23 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. $\endgroup$ – Wojowu Jan 23 at 16:29

$\begingroup$ @Wojowu "definitely not easy" if the answer is "yes". But it is conceivable that there is an easy "no"... $\endgroup$ – Goldstern Jan 26 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 ) $\endgroup$ – Wojowu Jan 26 at 9:46