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.
Gao , `` title Invariant Descriptive Set Theory '', Chapman & Hall/CRC Pure and Applied Mathematics, publisher CRC Press ( year 2008 )
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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.