  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 satisfying the standard
properties of the topological one, 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.
