Descriptive complexity of countable unions of Borel rectangles

Dominique Lecomte, Miroslav Zeleny

We give, for each countable ordinal $\xi \ge 1$, an example of a ${\mathbf{\Delta }}_2^0$ countable union of Borel rectangles that cannot be decomposed into countably many ${\mathbf{\Pi }}_{\xi }^0$ rectangle…