Baire reflection

We study reflection principles involving nonmeager sets and the Baire Property which are consequences of the generic supercompactness of $\omega_2$, such as the principle asserting that any point countable Baire space has a stationary set of closed subspaces of weight $\omega_1$ which are also Baire spaces. These principles entail the analogous principles of stationary reflection but are incompatible with forcing axioms. Assuming $MM$, there is a Baire metric space in which a club of closed subspaces of weight $\omega_1$ are meager in themselves. Unlike stronger forms of Game Reflection, these reflection principles do not decide $CH$, though they do give $\omega_2$ as an upper bound for the size of the continuum.