Descriptive complexity of countable unions of Borel rectangles
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چکیده
We give, for each countable ordinal ξ ≥ 1, an example of a ∆2 countable union of Borel rectangles that cannot be decomposed into countably many Πξ 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 ∆ξ-measurable countable coloring. 2010 Mathematics Subject Classification. Primary: 03E15, Secondary: 54H05
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تاریخ انتشار 2013