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.
['Reinhard Diestel', 'Oleg Pikhurko']
On the Cofinality of Infinite Partially Ordered Sets: Factoring a Poset into Lean Essential Subsets