Hennessy-Milner Theorem says that For two image-finite models M,N, we have that the pointed models M,w and N,v are equivalent in semantics (all holds on M,w holds on N,v and vice versa) iff M,w and N,v are bisimilar.
Then I wonder whether the conclusion holds if we only restrict one side is image-finite. My intuition is that it cannot hold, and especially, we can find an image-finite model and a non-image-finite model, where the two are equivalent in semantics but not in structure.
But the problem I met is that it's hard to find such an example. I've tried a lot but always failed eventually. Thanks for your help.
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