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arxiv: 0911.0068 · v1 · pith:C6Q54UT6new · submitted 2009-10-31 · 🧮 math.LO · math.CT

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
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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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