The logic μ(U) is the fixpoint extension of the “Until”-only fragment of linear-time temporal logic. It also happens to be the stutter-invariant fragment of linear-time μ-calculus μ(♦). We provide complete axiomatizations of μ(U) on the class of finite words and on the class of ω-words. We introduce for this end another logic, which we call μ(♦Γ), and which… (More)