## On the expressivity of the modal mu-calculus

**Julian Bradfield**
*Abstract:* We analyse the complexity of the sets of
states, in certain classes of infinite systems, that satisfy
formulae of the modal mu-calculus. Improving on some of our earlier
results, we establish a strong upper bound (namely
*Delta*^{1}_{2}). We also establish various
lower bounds and restricted upper bounds, incidentally providing
another proof that the mu-calculus alternation hierarchy does not
collapse at level 2.

**ECS-LFCS-95-338**, December 1995.

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