On Dilworth's decomposition theorem
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For every countable po set P without infinite chains there exists a partition (C"j: [email protected]) of P into pairwise disjoint chains and an antichain A such that C"[email protected]?A O for every [email protected]
[1] R. P. Dilworth,et al. A DECOMPOSITION THEOREM FOR PARTIALLY ORDERED SETS , 1950 .