Thomas Jech, Saharon Shelah
Abstract
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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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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.
Key concepts: Mathematics, Partition (number theory), Omega, Homogeneous, Combinatorics, Partition of unity, Pure mathematics, Set (abstract data type)