• Corpus ID: 51797199

On special partitions of Dedekind- and Russell-sets

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