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Proceedings of the American Mathematical Society

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Ordinal sum-sets


Author: Martin M. Zuckerman
Journal: Proc. Amer. Math. Soc. 35 (1972), 242-248
MSC: Primary 04A10
DOI: https://doi.org/10.1090/S0002-9939-1972-0314626-X
MathSciNet review: 0314626
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Abstract: A finite set, B, of ordinals will be called a sum-set if there are nonzero ordinals $ {\alpha _1},{\alpha _2}, \cdots ,{\alpha _n}$ such that the set of sums of $ {\alpha _1},{\alpha _2}, \cdots ,{\alpha _n}$, in all n! permutations of the summands, is B. Let $ {B_k}$ denote an arbitrary k-element sum-set; we consider various matters related to the set of numbers n for which there are n summands for $ {B_k}$.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0314626-X
Keywords: Ordinal addition, Cantor normal form, permutations of summands
Article copyright: © Copyright 1972 American Mathematical Society

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