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Jun 23, 2021 at 14:06 comment added user254885 thank you, it is very illuminating but indeed,does not say much about the filter ... A way to rephrase your definition is to say that $\mathcal F ^k(I)$ is is the collection of k-uniform hypergraphs on the vertex set I without infinite anticliques. (just a slight change of terminology)
Jun 20, 2021 at 16:56 history edited Gabe Conant CC BY-SA 4.0
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Jun 20, 2021 at 16:37 history answered Gabe Conant CC BY-SA 4.0