Given a Polish space [Formula: see text] and a countable collection of analytic hypergraphs on [Formula: see text], I consider the [Formula: see text]-ideal generated by Borel anticliques for the hypergraphs in the family. It turns out that many of the quotient posets are proper. I investigate the forcing properties of these posets, certain natural operations on them, and prove some related dichotomies.

中文翻译：

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超图和适当的强迫

给定一个波兰空间 [Formula: see text] 和 [Formula: see text] 上的分析超图的可数集合，我认为 [Formula: see text] - 由 Borel anticliques 为该族中的超图生成的理想值。事实证明，许多商组是正确的。我研究了这些偏序的强迫性质，对它们的某些自然操作，并证明了一些相关的二分法。