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Odd-sized partitions of Russell-sets

โœ Scribed by Horst Herrlich; Eleftherios Tachtsis

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
113 KB
Volume
56
Category
Article
ISSN
0044-3050

No coin nor oath required. For personal study only.

โœฆ Synopsis

In the setting of ZF, i.e., Zermelo-Fraenkel set theory without the Axiom of Choice (AC), we study partitions of Russell-sets into sets each with exactly n elements (called n-ary partitions), for some integer n. We show that if n is odd, then a Russell-set X has an n-ary partition if and only if |X| is divisible by n. Furthermore, we establish that it is relative consistent with ZF that there exists a Russell-set X such that |X| is not divisible by any finite cardinal n > 1.

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