Connected modal logics

We introduce the concept of a connected logic (over S4) and show that each connected logic with the finite model property is the logic of a subalgebra of the closure algebra of all subsets of the real line R, thus generalizing theMcKinsey-Tarski theorem.As a consequence,weobtain that each intermediate logicwith thefinitemodel property is the logic of a subalgebra of the Heyting algebra of all open subsets of R.