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arXiv:1804.04490 [math.LO]AbstractReferencesReviewsResources

On Dividing by Two in Constructive Mathematics

Andrew Swan

Published 2018-04-12Version 1

A classic result due to Bernstein states that in set theory with classical logic, but without the axiom of choice, for all sets $X$ and $Y$, if $X \times 2 \cong Y \times 2$ then also $X \cong Y$. We show that this cannot be done in constructive mathematics by giving some examples of toposes where it fails.

Categories: math.LO, math.CO
Subjects: 03F50, 03E10, 03G30
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