Year: 2018
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Swan, Andrew
Institution: University of Amsterdam
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2797920547