  The Baire algebra of a topological space $X$ is the quotient of the algebra
of all subsets of $X$ modulo the meager sets. We show that this Boolean algebra
can be endowed with a natural closure operator, resulting in a closure algebra
which we denote ${\bf Baire}(X)$. We identify the modal logic of such algebras
to be the well-known system $\sf S5$, and prove soundness and strong
completeness for the cases where $X$ is crowded and either completely
metrizable and continuum-sized or locally compact Hausdorff. We also show that
every extension of $\sf S5$ is the modal logic of a subalgebra of ${\bf
Baire}(X)$, and that soundness and strong completeness also holds in the
language with the universal modality.
