The elementary Archimedean axiom in absolute geometry

Victor Pambuccian

doi:10.1007/s00022-019-0507-x

The elementary Archimedean axiom in absolute geometry

Victor Pambuccian

Humanities, Arts and Cultural Studies, School of (SHARCS)

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Absolute planes in which the elementary Archimedean axiom holds satisfy Aristotle’s axiom. Absolute planes satisfying both the elementary Archimedean axiom and Bachmann’s Lotschnittaxiom are Euclidean. The Corollary to Aristotle’s axiom is equivalent to Aristotle’s axiom.

Original language	English (US)
Article number	52
Journal	Journal of Geometry
Volume	110
Issue number	3
DOIs	https://doi.org/10.1007/s00022-019-0507-x
State	Published - Dec 1 2019

Keywords

Absolute plane geometry
Aristotle’s axiom
Euclidean parallel postulate
Lotschnittaxiom
elementary Archimedean axiom

ASJC Scopus subject areas

Geometry and Topology

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10.1007/s00022-019-0507-x

Cite this

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The elementary Archimedean axiom in absolute geometry

Abstract

Keywords

ASJC Scopus subject areas

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