Erdös graphs resolve Fine's canonicity problem

@article{Goldblatt2003ErdsGR,
  title={Erd{\"o}s graphs resolve Fine's canonicity problem},
  author={Robert Goldblatt and Ian M. Hodkinson and Yde Venema},
  journal={Bulletin of Symbolic Logic},
  year={2003},
  volume={10},
  pages={186-208}
}
¤ Abstract. We show that there exist 2 @0 equational classes of Boolean algebras with operators that are not generated by the complex algebras of any first-order definable class of relational structures. Using a variant of this construction, we resolve a long-standing question of Fine, by exhibiting a bimodal logic that is valid in its canonical frames, but is not sound and complete for any first-order definable class of Kripke frames (a monomodal example can then be obtained using simulation… CONTINUE READING

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