In this talk, we present an interactive semantics for derivations (i.e., formal proofs) in an infinitary extension of classical logic. The formulas of our language are possibly infinitary (i.e., not necessarily well-founded, and not necessarily finitely branching) trees labeled by logical connectives and propositional variables. We show that in our setting every recursive formula equation has a unique solution. As for derivations, we use an infinitary variant of the standard Tait-calculus to derive sequents. In our sequent calculus, derivations are defined to be possibly infinitary trees labeled by sequents and rules. The interactive semantics we introduce is somehow similar to Girard's ludics, inasmuch as it builds upon a suitable procedure of cut-elimination. We show a completeness theorem for derivations, that we call interactive completeness theorem.