TITLE: Does stationary reflection imply Mahloness?
QUESTION [13 upvotes]: Suppose $\kappa$ is strongly inaccessible and every stationary subset of $\kappa$ reflects.  Must $\kappa$ be Mahlo?
Remarks:

It is possible for every stationary subset of $\kappa$ to reflect, but $\kappa$ is only weakly inaccessible (and not strongly inaccessible).
If $V=L$ then the answer is "yes", and in fact $\kappa$ must be weakly compact.

REPLY [14 votes]: Not necessarily.  Here's a counterexample, but I'm sure it is a ridiculous overkill in consistency strength:
Suppose $\kappa$ is the least inaccessible limit of supercompact cardinals.  Then $\kappa$ is not Mahlo.  If $S \subseteq \kappa$ is stationary, then there is a stationary $T \subseteq S$ such that $T$ concentrates on some cofinality $\theta < \kappa$.  Taking a supercompact $\delta \in (\theta,\kappa)$ gives the reflection of $T$ by the usual argument.