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The group of the countable universal graph

Published online by Cambridge University Press:  24 October 2008

J. K. Truss
J. K. Truss
Affiliation:
Department of Mathematics, Paisley College of Technology, Paisley PA 1 2BE
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Extract

Let C be a set with at least two, and at most ℵ0, members, and for any set X let [X]2 denote the set of its 2-element subsets. If Γ is a countable set, and Fc is a function from [Γ]2 into C, then the structure Γc = (Γ, Fc) is called the countable universal C-coloured graph if the following condition is satisfied:

Whenever α is a map from a finite subset of Γ into C there is xεΓ–dom α such that (∀yεdom α) Fc {x, y} = α(y).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 98 , Issue 2 , September 1985 , pp. 213 - 245
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

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