It's now well known that Continuum Hypothesis (CH) is independent from standard axioms of set theory: one can assume that $c=\aleph\_1$ or assume that $c \neq \aleph\_1$. Let us assume the second case-then the natural queation rise:


What 'values' $c$ can take? I know that it's impossible that $c=\aleph\_{\omega}$? Is it possible to give simple criterium for a cardinal $\alpha$ to have a property: $c=\alpha$ in 
some model of set theory? In particular, is there a cardinal $\alpha$ defined not using the term $c$ for which we have $c<\alpha$? And the last question, is it possible for $c$ to be weakly inaccessible? 



Around Continuum Hypothesis
Any cardinal of uncountable cofinality can consistently be the cardinal of the continuum. In particular, it is consistent that the cardinal of the continuum is weakly inaccessible (assuming, of course, that inaccessible cardinals are consistent.) The relevant paper is Solovay's "$2^{\aleph\_0}$ can be anything it ought to be" but nowadays the result is also in standard textbooks. 


