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Pré-Publication, Document De Travail Année : 2013

Descriptive complexity of countable unions of Borel rectangles

Résumé

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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Dates et versions

hal-00852718 , version 1 (21-08-2013)

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Dominique Lecomte, Miroslav Zeleny. Descriptive complexity of countable unions of Borel rectangles. 2013. ⟨hal-00852718⟩
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