On the Bourbaki–Witt principle in toposes

  title={On the Bourbaki–Witt principle in toposes},
  author={A. Bauer and Peter LeFanu Lumsdaine},
  journal={Mathematical Proceedings of the Cambridge Philosophical Society},
  pages={87 - 99}
  • A. Bauer, P. Lumsdaine
  • Published 1 January 2012
  • Mathematics
  • Mathematical Proceedings of the Cambridge Philosophical Society
Abstract The Bourbaki–Witt principle states that any progressive map on a chain-complete poset has a fixed point above every point. It is provable classically, but not intuitionistically. We study this and related principles in an intuitionistic setting. Among other things, we show that Bourbaki–Witt fails exactly when the trichotomous ordinals form a set, but does not imply that fixed points can always be found by transfinite iteration. Meanwhile, on the side of models, we see that the… Expand
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