Herbrand's theorem and non-Euclidean geometry

Abstract : 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.
Document type :
Journal articles
Complete list of metadatas

Cited literature [5 references]  Display  Hide  Download

https://hal.inria.fr/hal-01071431
Contributor : Julien Narboux <>
Submitted on : Tuesday, February 24, 2015 - 9:20:53 AM
Last modification on : Saturday, October 27, 2018 - 1:28:02 AM
Long-term archiving on : Wednesday, May 27, 2015 - 10:10:54 AM

File

1410.2239v2.pdf
Files produced by the author(s)

Identifiers

Citation

Michael Beeson, Pierre Boutry, Julien Narboux. Herbrand's theorem and non-Euclidean geometry. Bulletin of Symbolic Logic, Association for Symbolic Logic, 2015, 21 (2), pp.12. ⟨10.1017/bsl.2015.6 ⟩. ⟨hal-01071431v3⟩

Share

Metrics

Record views

195

Files downloads

358