### A partition theorem for pairs of finite sets

by Jech and Shelah. [JeSh:392]

J American Math Soc, 1991

Every partition of [[omega_1]^{< omega}]^2 into
finitely many pieces has a cofinal homogeneous set. Furthermore,
it is consistent that every directed partially ordered set
satisfies the partition property if and only if it has finite
character.

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