On the failure of fixed-point theorems for chain-complete lattices in the effective topos
Copyright policy )On the failure of fixed-point theorems for chain-complete lattices in the effective topos
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.
- University of Ljubljana Slovenia
Chain-complete posets, Topoi, 03G30, 03G10, Mathematics - Category Theory, Constructive logic, Bourbaki-Witt theorem, Mathematics - Logic, Other constructive mathematics, Tarski’s theorem, Effective topos, Theoretical Computer Science, Fixed points, effective topos, Constructive fixed-point theorems, Bourbaki–Witt theorem, constructive logic, FOS: Mathematics, Tarski's theorem, Category Theory (math.CT), chain-complete posets, Logic (math.LO), fixed-point theorems, Computer Science(all)
Chain-complete posets, Topoi, 03G30, 03G10, Mathematics - Category Theory, Constructive logic, Bourbaki-Witt theorem, Mathematics - Logic, Other constructive mathematics, Tarski’s theorem, Effective topos, Theoretical Computer Science, Fixed points, effective topos, Constructive fixed-point theorems, Bourbaki–Witt theorem, constructive logic, FOS: Mathematics, Tarski's theorem, Category Theory (math.CT), chain-complete posets, Logic (math.LO), fixed-point theorems, Computer Science(all)
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