# Model for “$\kappa$ limit cardinal iff $2^\kappa$ limit cardinal”

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?

• A related question: mathoverflow.net/questions/226887/… – Will Brian Jan 23 at 16:00
• Actually, this comment to the answer is exactly the present question. – Pedro Sánchez Terraf Jan 23 at 16:18
• 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. – Wojowu Jan 23 at 16:29
• @Wojowu "definitely not easy" if the answer is "yes". But it is conceivable that there is an easy "no"... – Goldstern Jan 26 at 9:25
• @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 ) – Wojowu Jan 26 at 9:46