Complete Axiomatization of the Stutter-Invariant Fragment of the Linear-time mu-calculus Amélie Gheerbrant Abstract: The logic \mu(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 \mu-calculus \mu(\diamond). We provide complete axiomatizations of \mu(U) on the class of finite words and on the class of \omega-words. We introduce for this end another logic, which we call \mu(\diamond\Gamma), and which is a variation of \mu(\diamond) where the Next time operator is replaced by the family of its stutter-invariant counterparts. This logic has exactly the same expressive power as \mu(U). Using already known results for \mu(\diamond), we first prove completeness for \mu(\diamond\Gamma), which finally allows us to obtain completeness for \mu(U).