Herbrand’s theorem and non-Euclidean geometry
نویسندگان
چکیده
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 nonEuclidean 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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تاریخ انتشار 2015