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The elementary Archimedean axiom in absolute geometry

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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.

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Authors and Affiliations

  1. School of Mathematical and Natural Sciences (MC 2352), Arizona State University - West Campus, P. O. Box 37100, Phoenix, AZ, 85069-7100, USA

    Victor Pambuccian

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  1. Victor Pambuccian
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Correspondence to Victor Pambuccian.

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To the memory of Marvin Jay Greenberg (1935–2017)

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This paper was written while the author was a Fulbright Scholar at Yerevan State University in Yerevan, Armenia. Thanks are due to Franz Kalhoff, Rolf Struve, and Horst Struve for a close reading of the manuscript and for their corrections.

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Pambuccian, V. The elementary Archimedean axiom in absolute geometry. J. Geom. 110, 52 (2019). https://doi.org/10.1007/s00022-019-0507-x

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  • DOI: https://doi.org/10.1007/s00022-019-0507-x

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