Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-28T04:29:27.221Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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