On the Failure of Fixed-Point Theorems for Chain-complete Lattices in the Effective Topos
Logic
2012-01-05 v1 Category Theory
Abstract
In the effective topos there exists a chain-complete distributive lattice with a monotone and progressive endomap which does not have a fixed point. Consequently, the Bourbaki-Witt theorem and Tarski's fixed-point theorem for chain-complete lattices do not have constructive (topos-valid) proofs.
Keywords
Cite
@article{arxiv.0911.0068,
title = {On the Failure of Fixed-Point Theorems for Chain-complete Lattices in the Effective Topos},
author = {Andrej Bauer},
journal= {arXiv preprint arXiv:0911.0068},
year = {2012}
}