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The chain covering number of a poset with no infinite antichains
The chain covering number \Cov(P) of a poset is the least number of
chains needed to cover . For a cardinal , we give a list of posets of
cardinality and covering number such that for every poset with no
infinite antichain, \Cov(P)\geq \nu if and only if embeds a member of the
list. This list has two elements if is a successor cardinal, namely
and its dual, and four elements if is a limit cardinal with
\cf(\nu) weakly compact. For , a list was given by the first
author; his construction was extended by F. Dorais to every infinite successor
cardinal .Comment: P page