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# Ordinal Sum-Sets

Martin M. Zuckerman
Proceedings of the American Mathematical Society
Vol. 35, No. 1 (Sep., 1972), pp. 242-248
DOI: 10.2307/2038479
Stable URL: http://www.jstor.org/stable/2038479
Page Count: 7
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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 $B_k$.

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