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Partial well-ordering of sets of vectors

Published online by Cambridge University Press:  26 February 2010

R. Rado
R. Rado
Affiliation:
King's College, London
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Extract

Graham Higman (1) has investigated quasi-order [(2), p. 4] relations a ≤ b on a set S which, in his terminology, have the following finite basis property:

If A ⊂ S, then there is a finite set B ⊂ A such that, given any a α A, there is some b α B satisfying b ≤ a.

Type
Research Article
Information
Mathematika , Volume 1 , Issue 2 , June 1954 , pp. 89 - 95
Copyright
Copyright © University College London 1954

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References

1.Higman, Graham, “Ordering by divisibility in abstract algebra”, Proc. London Math. Soc. (3), 2 (1952), 326–336.CrossRefGoogle Scholar
2.Birkhoff, G., Lattice theory, second edition (1948).Google Scholar
3.Erdös, P. and Rado, R., “Sets having a divisor property”, American Math. Monthly, 57 (1952), 255–257.Google Scholar
4.Kruskal, J. Jr., Proc. International Congress of Math. (1954), II, 35.Google Scholar