Herbrand's theorem and non-Euclidean geometry

Michael Beeson; Pierre Boutry; Julien Narboux

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arXiv · 1410.2239

Herbrand's theorem and non-Euclidean geometry

Michael Beeson·Pierre Boutry·Julien Narboux

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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.

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BibTeX RIS

Michael Beeson, Pierre Boutry, Julien Narboux. 2014-10-07. Herbrand's theorem and non-Euclidean geometry. https://arxiv.org/abs/1410.2239

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