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Rearranging transfinite series of ordinals

Published online by Cambridge University Press:  17 April 2009

Péter Komjath
Péter Komjath
Affiliation:
Department of Algebra and Number Theory, Eötvös Lorand University, Budapest, Hungary.
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Abstract

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A new, simplified proof is given of a theorem of J.L. Hickman (to be published; see also J. London Math. Soc. (2) 9 (1974), 239–244), giving an upper bound for the sums of a well-ordered series of ordinals under permutation.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 16 , Issue 3 , June 1977 , pp. 321 - 323
Copyright
Copyright © Australian Mathematical Society 1977

References

[1]Ginsburg, S., “On the distinct sums of λ-type transfinite series obtained by permuting the elements of a fixed λ-type series”, Fund. Math. 39 (1952), 131–132.CrossRefGoogle Scholar
[2]Hickman, J.L., “Concerning the number of sums obtainable from a countable series of ordinals by permutations that preserve the order-type”, J. London Math. Soc. (2) 9 (1974/1975), 239–244.CrossRefGoogle Scholar
[3]Hickman, J.L., “Some results on series of ordinals”, Z. math. Logik Grundlagen Math. (to appear).Google Scholar
[4]Sierpiński, Wacław, “Sur les séries infinies de nombres ordinaux”, Fund. Math. 36 (1949), 248–253.CrossRefGoogle Scholar