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Journal articles

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.
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https://hal.inria.fr/hal-01071431
Contributor : Julien Narboux Connect in order to contact the contributor
Submitted on : Tuesday, February 24, 2015 - 9:20:53 AM
Last modification on : Wednesday, December 1, 2021 - 3:32:11 PM
Long-term archiving on: : Wednesday, May 27, 2015 - 10:10:54 AM

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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⟩

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