Forcing ${\mathbf{\Sigma }}_1^1$-Separation on ${\omega }_1^{{\omega }_1}$

We prove that it is consistent that every two disjoint boldface ${\mathbf{\Sigma }}_1^1$ subsets of ${\omega }_1^{{\omega }_1}$ can be separated by a boldface ${\mathbf{\Delta }}_1^1$ set. The forcing starts from $L$ and preserves CH and therefore also ${\omega }_1^{<{\omega }_1}={\omega }_1$.