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Journal Articles Bulletin of Symbolic Logic Year : 2015

Herbrand's theorem and non-Euclidean geometry


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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Dates and versions

hal-01071431 , version 1 (05-10-2014)
hal-01071431 , version 2 (08-10-2014)
hal-01071431 , version 3 (24-02-2015)



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