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

@article{citeulike:6061346, 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.}, archivePrefix = {arXiv}, author = {Bauer, Andrej}, citeulike-article-id = {6061346}, citeulike-linkout-0 = {http://arxiv.org/abs/0911.0068}, citeulike-linkout-1 = {http://arxiv.org/pdf/0911.0068}, day = {31}, eprint = {0911.0068}, keywords = {category-theory, computation, mathematics, topos-theory}, month = {Oct}, posted-at = {2009-11-03 19:22:36}, priority = {2}, title = {On the Failure of Fixed-Point Theorems for Chain-complete Lattices in the Effective Topos}, url = {http://arxiv.org/abs/0911.0068}, year = {2009} }

TY - JOUR ID - citeulike:6061346 L3 - citeulike-article-id:6061346 N2 - 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. TI - On the Failure of Fixed-Point Theorems for Chain-complete Lattices in the Effective Topos KW - category-theory KW - computation KW - mathematics KW - topos-theory AU - Bauer, Andrej PY - 2009/Oct/31/ UR - http://arxiv.org/abs/0911.0068 ER -