Is is consistent that $\aleph_1 < \text{cov(meager)} < 2^{\aleph_0}$?
I can only seem to find references for results that assert it is consistent that it (or other cardinal characteristics) is $\aleph_1$ or $2^{\aleph_0}$.
If this is possible could someone provide a reference or sketch the argument. Thanks.
Start with a model where continuum is large, say $\omega_5$. Then do a finite support iteration of random forcing of length $\omega_2$. This is ccc so continuum is at least $\omega_5$. The Cohen reals appearing at stages of cofinality $\omega$ will ensure that $\omega_1$ meager sets cannot cover all reals and the $\omega_2$-many meager sets coded by the random reals will cover all reals.
An interesting fact about covering numbers: While Arnie Miller has shown that the cofinality of covering of the meager ideal is always uncountable, a famous result of Shelah is that the covering of the null ideal could be $\omega_{\omega}$.