Original Articles

Binary Partitions in the Absence of Choice or Rearranging Russell's Socks

Published in: Quaestiones Mathematicae
Volume 30 , issue 4 , 2007 , pages: 465–470

DOI: 10.2989/16073600709486213

Author(s): Horst Herrlich

Keywords: BINARY PARTITIONS , AXIOM OF CHOICE , DEDEKIND-CARDINALS , RUSSELL-CARDINALS , EVEN CARDINALS

Abstract

Given a sequence (X_n )n∈N of pairwise disjoint 2-element sets. Can ∪_n∈N X_n be rearranged as a union ∪_i∈I Y_i of a family (Y_i )i∈I of pairwise disjoint 2-element sets, indexed by an uncountable set I? It will be shown that in the absence of the Axiom of Choice, this strange phenomenon can indeed occur.

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