On the Failure of Fixed-Point Theorems for Chain-complete Lattices in the Effective Topos
classification
🧮 math.LO
math.CT
keywords
chain-completeeffectivefixed-pointlatticestheoremtoposbourbaki-wittconsequently
read the original 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.
This paper has not been read by Pith yet.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.