Model checking and static analysis are both successful approaches to the analysis of IT systems and it has been shown that many static analyses can be reduced to model checking. Recent results show that CTL model checking can be reduced to static analysis and that the set of satisfying states of a CTL formula can be described as the least element in a Moore family of acceptable sets of states for the static analysis. Turning the attention to the μ-calculus we are able to generalise this result to the alternation-free fragment whereas even for the fragment of alternation depth 2 we show that the fixed point characterisation cannot be recast as a Moore family property.