Section: New Results

Formalization of the Poincaré disk model in Isabelle

Participants : Pierre Boutry, Danijela Simić [University of Belgrade] , Filip Marić [University of Belgrade] .

The Poincaré disk model is a model that can be shown to satisfy all axioms of Tarski's system of geometry at the exception of the parallel postulate. We developed a formal proof of this fact in the Isabelle system and submitted an article for publication. Reviewers suggested that we add a proof that the postulate of the existence of limiting parallels does hold. This completes neatly the work on this topic, as it allows us to exhibit that the Poincaré disk model is not only a counter-model for the parallel postulate but also a model of hyperbolic geometry. An improved version of the article will be submitted soon.