I know that "ZFC+the existence of an inaccessible cardinal" is equconsistent to

"ZFC + every $\mathbf{\Sigma}^1_3$ set is measurable".

Then how about the light face case?

Without large cardinal assumption, can we have a ZFC model in which every analytical set (or lightface $\Sigma^1_3$) is measurable?

Here a set is analytical if it is $\Sigma^1_n$ for some $n$.

Edited:

This was already answered by Shelah. ''It is known that there is a generic extension of $L$ not collapsing cardinals nor violating CH, in which every definable (with no parameter!) set of reals is measurable..." from the 3rd remark, page 18, Shelah's paper.