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For a closed subset I of the interval [0,1] we let A(I) = [v1(I),C(I)](1/2)2. We show that A(I) is isometric to a 1-complemented subspace of A(0,1), and that the Szlenk index of A(I) is larger than the Cantor index of I. We also investigate, for ordinals η < ω1, the bases structures of A(η), A*(η), and $A_{*}\left(\eta \right)$ [the isometric predual of A(η)]. All the results of this paper extend, with obvious changes in the proofs, to the interpolation spaces ${[v_1\left(I\right),C\left(I\right)]}_{\theta q}$.