### A class of ${l}^{1}$-preduals which are isomorphic to quotients of $C\left({\omega}^{\omega}\right)$

For every countable ordinal α, we construct an ${l}_{1}$-predual ${X}_{\alpha}$ which is isometric to a subspace of $C\left({\omega}^{{\omega}^{{\omega}^{\alpha}+2}}\right)$ and isomorphic to a quotient of $C\left({\omega}^{\omega}\right)$. However, ${X}_{\alpha}$ is not isomorphic to a subspace of $C\left({\omega}^{{\omega}^{\alpha}}\right)$.