The chain covering number of a poset with no infinite antichains

Uri Abraham, Maurice Pouzet

Research output: Contribution to journalArticlepeer-review


The chain covering number Cov(P) of a poset P is the least number of chains needed to cover P. For an uncountable cardinal ν, we give a list of posets of cardinality and covering number ν such that for every poset P with no infinite antichain, Cov(P) ≥ ν if and only if P embeds a member of the list. This list has two elements if ν is a successor cardinal, namely [ν]2 and its dual, and four elements if ν is a limit cardinal with cf(ν) weakly compact. For ν = ℵ1, a list was given by the first author; his construction was extended by F. Dorais to every infinite successor cardinal ν.

Original languageEnglish
Pages (from-to)1383-1399
Number of pages17
JournalComptes Rendus Mathematique
StatePublished - 1 Jan 2023

ASJC Scopus subject areas

  • General Mathematics


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