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Partition Relations for Ordinal Numbers

Published online by Cambridge University Press:  20 November 2018

E. C. Milner
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Capital letters denote sets and the cardinal of A is |A|. Greek letters always denote ordinal numbers and, unless stated otherwise, small latin letters denote non-negative integers. The symbol [A]r is used to denote the set {X: X ⊂ A; |X| = r} of all subsets of A with relements. If A is a simply ordered set with the order relation <, then the order type of A with this ordering is written as tp <A or simply as tp A when there is no ambiguity about the intended order relation. A graph G = (A, E) is an ordered pair with A as the set of vertices and E ⊂ [A]2 as the set of edges. In particular, if A is simply ordered, we call G a graph of type tp A. A complete subgraph of G = (A, E)is a set B ⊂ A such that [B]2 ⊂ E; a set C⊂ A is independent if [C]2 ∩ E = ∅.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 317 - 334
Copyright
Copyright © Canadian Mathematical Society 1969

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