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Partial well-ordering of sets of vectors

  • R. Rado (a1)
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Graham Higman (1) has investigated quasi-order [(2), p. 4] relations ab on a set S which, in his terminology, have the following finite basis property:

If AS, then there is a finite set BA such that, given any a α A, there is some b α B satisfying ba.

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1.Higman, Graham, “Ordering by divisibility in abstract algebra”, Proc. London Math. Soc. (3), 2 (1952), 326336.
2.Birkhoff, G., Lattice theory, second edition (1948).
3.Erdös, P. and Rado, R., “Sets having a divisor property”, American Math. Monthly, 57 (1952), 255257.
4.Kruskal, J. Jr., Proc. International Congress of Math. (1954), II, 35.
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Mathematika
  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
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