Transfinite dependent choice and w-model reflection

In this paper we present some metapredicative subsystems of analysis. We deal with reflection principles, omega-model existence axioms (limit axioms) and axioms asserting the existence of hierarchies, We show several equivalences among the introduced subsystems. In particular we prove the equivalence of Sigma\ transfinite dependent choice and Pi(2)(1) reflection on omega-models of Sigma\-DC.