S4.3 and hereditarily extremally disconnected spaces Guram Bezhanishvili, Nick Bezhanishvili, Joel Lucero-Bryan, Jan van Mill Abstract: The modal logic S4.3 defines the class of hereditarily extremally disconnected spaces (HED-spaces). We construct a countable HED-subspace X of the Gleason cover of the real closed unit interval [0; 1] such that S4.3 is the logic of X.