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It is shown that every separable reflexive Banach space is a quotient of a reflexive hereditarily indecomposable space, which yields that every separable reflexive Banach is isomorphic to a subspace of a reflexive indecomposable space. Furthermore, every separable reflexive Banach space is a quotient of a reflexive complementably l-saturated space with I < p < ∞ and of a Cu saturated space

The cofinal property of the reflexive indecomposable Banach spaces