Constant Modal Logics and Canonicity
If a modal logic is valid in its canonical frame, and its class of
validating frames is invariant under bounded epimorphisms (or equivalently,
closed under images of bisimulations), then the logic is axiomatizable by
variable-free formulas. Hence its class of frames is first-order definable.
Written as a tribute to Krister Segerberg on his 70th birthday.