Herbrand's theorem and non-Euclidean geometry
Logic
2015-11-10 v2
Abstract
We use Herbrand's theorem to give a new proof that Euclid'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.
Cite
@article{arxiv.1410.2239,
title = {Herbrand's theorem and non-Euclidean geometry},
author = {Michael Beeson and Pierre Boutry and Julien Narboux},
journal= {arXiv preprint arXiv:1410.2239},
year = {2015}
}
Comments
12 pages, 5 figures