# On special partitions of Dedekind- and Russell-sets

@inproceedings{Herrlich2012OnSP, title={On special partitions of Dedekind- and Russell-sets}, author={Horst Herrlich and Paul E. Howard and Eleftherios Tachtsis}, year={2012} }

A Russell set is a set which can be written as the union of a countable pairwise disjoint set of pairs no infinite subset of which has a choice function and a Russell cardinal is the cardinal number of a Russell set. We show that if a Russell cardinal a has a ternary partition (see Section 1, Definition 2) then the Russell cardinal a + 2 fails to have such a partition. In fact, we prove that if a ZF-model contains a Russell set, then it contains Russell sets with ternary partitions as well as…

## 3 Citations

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