• DOI:10.46298/lmcs-18(1:30)2022
• Corpus ID: 221970991

Fixed Points Theorems for Non-Transitive Relations

@article{Dubut2022FixedPT,
  title={Fixed Points Theorems for Non-Transitive Relations},
  author={J{\'e}r{\'e}my Dubut and Akihisa Yamada},
  journal={Log. Methods Comput. Sci.},
  year={2022},
  volume={18}
}

• Jérémy Dubut, A. Yamada
• Published 28 September 2020
• Mathematics
• Log. Methods Comput. Sci.

In this paper, we develop an Isabelle/HOL library of order-theoretic fixed-point theorems. We keep our formalization as general as possible: we reprove several well-known results about complete orders, often with only antisymmetry or attractivity, a mild condition implied by either antisymmetry or transitivity. In particular, we generalize various theorems ensuring the existence of a quasi-fixed point of monotone maps over complete relations, and show that the set of (quasi-)fixed points is itself complete. This result generalizes and strengthens theorems of Knaster-Tarski, Bourbaki-Witt, Kleene, Markowsky, Pataraia, Mashburn, Bhatta-George, and Stouti-Maaden.