Descriptive complexity of countable unions of Borel rectangles

Dominique Lecomte; Miroslav Zeleny

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arXiv · 1308.4540

Descriptive complexity of countable unions of Borel rectangles

Dominique Lecomte·Miroslav Zeleny

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Abstract

We give, for each countable ordinal $\xi \geq 1$, an example of a ${\bf\Delta}^0_2$ countable union of Borel rectangles that cannot be decomposed into countably many ${\bf\Pi}^0_\xi$ rectangles. In fact, we provide a graph of a partial injection with disjoint domain and range, which is a difference of two closed sets, and which has no ${\bf\Delta}^0_\xi$-measurable countable coloring.

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Dominique Lecomte, Miroslav Zeleny. 2013-08-21. Descriptive complexity of countable unions of Borel rectangles. https://arxiv.org/abs/1308.4540

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