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arXiv · 1804.04490

On Dividing by Two in Constructive Mathematics

Andrew Swan
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Abstract

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.

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Andrew Swan. 2018-04-12. On Dividing by Two in Constructive Mathematics. https://arxiv.org/abs/1804.04490

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