= Finite-symmetric-difference colouring of infinite subsets
Choose a representative $R$ of each class of countably infinite <sets> modulo <finite symmetric difference>, and colour $A$ by the parity of $|A\mathbin\triangle R|$. Removing one element stays in the same class and flips the parity. Every infinite candidate homogeneous set therefore has two countably infinite subsets of opposite colours. With <choice>, this refutes unrestricted countably infinite-arity positive <partition relations> on every infinite cardinal.
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