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A note on Dilworth’s theorem in the infinite case. (English) Zbl 0629.06002

The interesting work done in this paper was inspired by the following theorem of Dilworth: if every antichain in a poset has size \(\leq k\) (k is finite), then the poset is the union of at most k chains. The main result of this paper: if P is a poset and every antichain is finite (without assumption of existence of a finite bound on the size of the antichains), and if the length of the well-founded poset of antichains is less than \(\omega^ 2_ 1\), then P is the union of countably many chains.
Reviewer: L.Esakia

MSC:

06A06 Partial orders, general
03E10 Ordinal and cardinal numbers
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References:

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