Abstract
We study which infinite posets have simple cofinal subsets such as chains, or decompose canonically into such subsets. The posets of countable cofinality admitting such a decomposition are characterized by a forbidden substructure; the corresponding problem for uncountable cofinality remains open.
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Diestel, R., Pikhurko, O. On the Cofinality of Infinite Partially Ordered Sets: Factoring a Poset into Lean Essential Subsets. Order 20, 53–66 (2003). https://doi.org/10.1023/A:1024449306316
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DOI: https://doi.org/10.1023/A:1024449306316