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We show that the ordering of the Hanf number of L_{omega, omega}(wo) (wellordering), L^c_{omega, omega} (quantification on countable sets), L_{omega,omega}(aa) (stationary logic) and second order logic, have no more restraintsprovable in ZFC than previously known (those independence proofs assumeCON(ZFC) only). We also get results on corresponding logics for L_{lambda, mu}.

The Hanf numbers of stationary logic. II. Comparison with other logics.