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arXiv:math/0605779math.LO

Division by three

Peter G. Doyle, John Horton Conway

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Abstract

We prove without appeal to the Axiom of Choice that for any sets A and B, if there is a one-to-one correspondence between 3 cross A and 3 cross B then there is a one-to-one correspondence between A and B. The first such proof, due to Lindenbaum, was announced by Lindenbaum and Tarski in 1926, and subsequently `lost'; Tarski published an alternative proof in 1949. We argue that the proof presented here follows Lindenbaum's original.

arXiv comments
Version dated 1994
Journal reference
DOI
Subjects
math.LOLogic math.COCombinatorics

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