IK is the IK-bisimulation-invariant fragment of intuitionistic first-order logic, accompanied by a Hennessy-Milner theorem and intuitionistic analogues of Los's theorem, elementary embeddings, and countable saturation.
Journal of Applied Non-Classical Logics20(3), pp
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Intuitionistic K is a Bisimulation-Invariant Fragment of Intuitionistic First-Order Logic
IK is the IK-bisimulation-invariant fragment of intuitionistic first-order logic, accompanied by a Hennessy-Milner theorem and intuitionistic analogues of Los's theorem, elementary embeddings, and countable saturation.