2 problems

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Lecomte–Zeleny dichotomy conjecture for separation by Borel rectangles
Let $0<\xi<\omega_1$ . For each such $\xi$ , let $\mathbb{X}_\xi$ and $\mathbb{Y}_\xi$ be Polish spaces, and let…
Conjectureopenanalytic-sets borel-hierarchy descriptive-set-theoryarXiv posted 2 days ago
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The coincidence of the weak index and Borel hierarchies for weakly recognizable languages
Weak index–Borel hierarchy conjecture. For weakly recognizable languages, the weak index hierarchy and the Borel hierarchy coincide; equivalently, every weakly recognizable…
Conjectureopenautomata-theory borel-hierarchy descriptive-set-theoryarXiv posted 2 days ago

Lecomte–Zeleny dichotomy conjecture for separation by Borel rectangles