✦ LIBER ✦

Theorems on intervals of ordered sets

✍ Scribed by Richard Rado

Publisher: Elsevier Science
Year: 1981
Tongue: English
Weight: 193 KB
Volume: 35
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(81)90208-9

No coin nor oath required. For personal study only.

✦ Synopsis

VE I) be a family of such intervals. For NE I let V(N) be the chromatic number of the intersection graph 0; (A,,: Y E N), Theorem 1. Zf I is finite and A,, f1.4,,#0 for CL, YE I, tlren n,,, A# 6 Theorem 2. Let k IX a positiw integer and x(N) G k for INI = k + 1. Then x(Z) c k. XlleOrean 3. There is JEZ with CJVEJ& = iJvEI & and x(J) finire if and only if there is a well-order of I in w%i&. for every xc U YEI A, the set {v: x E &} has a lust elenrenf.

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