Aleph-one-Suslin decomposition into analytic sets (${\aleph }_1$-Suslin)

Every ${\aleph }_1$-Suslin set is a union of ${\aleph }_1$ analytic sets. Every countable sequence of countable ordinals is bounded below ${\omega }_1$, and after restricting all labels below one countable ordinal the first-coordinate space can be recoded by $\omega$.