Independence of a Certain Axiomatic System

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Aug 1969Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 22, page 470 (issn: 0002-9939,

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Authors: Gutierrez-Novoa, L.;

doi: 10.2307/2037080 , 10.1090/s0002-9939-1969-0243407-0

Independence of a Certain Axiomatic System

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Abstract

To prove the independence of the system of axioms introduced in [1 ] we exhibit here ten models, each of them satisfying all the axioms but one; e.g. model M5 fails to satisfy P5 of [1]. We call model F the Euclidean 3-space with the usual vector structure, introduce a suitable order function 4 and the usual notion of orthogonality. Let Ai(i = 1, 2, 3, 4) be the position vectors of four points and define:

Keywords

foundations of geometry

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