Systems of equations with sets of integers as unknowns are considered, with the operations of union, intersection and addition of sets, . These equations were recently studied by the authors (“Representing hyper-arithmetical sets by equations over sets of integers”, Theory of Computing Systems , 51 (2012), 196–228), and it was shown that the class of sets representable by their unique solutions is exactly the class of hyper-arithmetical sets. In this paper it is demonstrated that greatest solutions of such equations represent exactly the -sets in the analytical hierarchy, and all those sets can already be represented by systems in the resolved form Xi=φi(X1,…,Xn). Least solutions of such resolved systems represent exactly the recursively enumerable sets.