Separation of analytic sets by rectangles of low complexity

Abstract

We provide Hurewicz tests for the separation of disjoint analytic sets by rectangles of the form $\Gamma \times {\Gamma }^{\prime }$ for $\Gamma ,{\Gamma }^{\prime }\in {\mathbf{\Sigma }}_1^0,{\mathbf{\Pi }}_1^0,{\mathbf{\Pi }}_2^0$.