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Combinatorial properties of infinite sets. This is a corner-point of set theory and combinatorics.
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a filter of subsets intersecting the cartesian power of each infinite subset
Is the following filter known in set theory, and does it have a name ?
For $k=1$ it is the filter of cofinite subsets.
Fix a natural number $k$ and a linear order $I$.
Define a filter on the set of s …