Log-euclidean geometry and "Grundlagen der Geometrie" - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2019

Log-euclidean geometry and "Grundlagen der Geometrie"

Abstract

We define the simplest log-euclidean geometry. This geometry exposes a difficulty hidden in Hilbert's list of axioms presented in his "Grundlagen der Geometrie". The list of axioms appears to be incomplete if the foundations of geometry are to be independent of set theory, as Hilbert intended. In that case we need to add a missing axiom. Log-euclidean geometry satisfies all axioms but the missing one, the fifth axiom of congruence and Euclid's axiom of parallels. This gives an elementary proof (with no need of Riemannian geometry) of the independence of these axioms from the others.

Domains

Logic [math.LO]
Fichier principal
Vignette du fichier
grundlagen.pdf (63.39 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-02369425 , version 1 (19-11-2019)

Identifiers

Cite

Ricardo Pérez-Marco. Log-euclidean geometry and "Grundlagen der Geometrie". 2019. ⟨hal-02369425⟩
53 View
46 Download

Altmetric

Share

Gmail Facebook X LinkedIn More