= Halpern–Läuchli theorem
{wiki=Halpern–Läuchli_theorem}
The Halpern–Läuchli theorem is a result in set theory and combinatorial set theory, particularly dealing with partition theorems. It provides insights into the behavior of certain sets under the action of partitioning and relates to properties of infinite sets. In basic terms, the theorem states that if we have a sufficiently large set \\(X\\) and we partition it into finitely many pieces, then at least one of these pieces will contain a large homogeneous subset.
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