Fixed-Point Theorems for Non-Transitive Relations
26 February 2024
On Monday 26th of February, at 15:00, Jérémy Dubut-Kross will give a talk on "Fixed-Point Theorems for Non-Transitive Relations" during the seminar of the Automata and Application group.
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. Joint work with Akihisa Yamada.