Bisimilarity on NLMP is analytic in general, Borel for well-founded cases, and not characterizable by any countable fragment of basic modal logic with denumerable conjunctions.
Kechris , `` title Classical Descriptive Set Theory '', series Graduate Texts in Mathematics volume 156 , publisher Springer-Verlag ( year 1994 )
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The complexity of bisimilarity on pointmass processes
Bisimilarity on NLMP is analytic in general, Borel for well-founded cases, and not characterizable by any countable fragment of basic modal logic with denumerable conjunctions.