On Dividing by Two in Constructive Mathematics
Logic
2018-04-13 v1 Combinatorics
Abstract
A classic result due to Bernstein states that in set theory with classical logic, but without the axiom of choice, for all sets and , if then also . We show that this cannot be done in constructive mathematics by giving some examples of toposes where it fails.
Keywords
Cite
@article{arxiv.1804.04490,
title = {On Dividing by Two in Constructive Mathematics},
author = {Andrew Swan},
journal= {arXiv preprint arXiv:1804.04490},
year = {2018}
}