Herbrand's theorem and non-Euclidean geometry
Résumé
We use Herbrand's theorem to give a new proof that Eu- clid's parallel axiom is not derivable from the other axioms of first-order Euclidean geometry. Previous proofs involve constructing models of non- Euclidean geometry. This proof uses a very old and basic theorem of logic together with some simple properties of ruler-and-compass constructions to give a short, simple, and intuitively appealing proof.
Domaines
Logique en informatique [cs.LO]
Origine : Fichiers produits par l'(les) auteur(s)