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Remarks on the cofinality of a partially ordered set, and a generalization of König's lemma

✍ Scribed by E.C. Milner; N. Sauer

Publisher
Elsevier Science
Year
1981
Tongue
English
Weight
694 KB
Volume
35
Category
Article
ISSN
0012-365X

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✦ Synopsis

A problem concerning the cardinality of the cofinal subsets of a partially ordered set is reduced to an open problem irr graph tteory. Let A be an in&it: wdinal, V = Ui,, Vi, I Uiii VJC IVJ (i CA). J_et G be a graph on V with the proper?y that whenever i <A, x=u ie,cA Vi and IXICIVil, then there is a set Y c Vi such that IY1 = IVj and Y XX eE(G).

The question is whether such a gaph contains a complete subgraph of cardinality A? We :?iqve an extension of Kikig's infinitary lemma which shows that the above graph contains a "PL?: of cardinal A.

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