On the Failure of Fixed-Point Theorems for Chain-complete Lattices in the Effective Topos

Details On the Failure of Fixed-Point Theorems for Chain-complete Lattices in the Effective Topos On the Failure of Fixed-Point Theorems for Chain-complete Lattices in the Effective Topos

2009-10-31

arxiv.org/abs/0911.0068v1

Mathematics

Logic

Scientific paper

10.1016/j.tcs.2011.12.005

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.

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