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<p>Tarski’s language for plane absolute geometry has points, equidistance, and betweenness as the only primitive notions. We present an axiom system for plane absolute geometry in Tarski’s language that takes Euclid’s Fourth Postulate as an axiom, but has no congruence axioms of the Side-Angle-Side type for arbitrary triangles. The axiom system presented here validates a statement made by Beppo Levi in 1947.</p>

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Absolute geometry with the fourth postulate

  • 期刊论文

  • 发表日期：

    2026年4月9日

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  • Sheila K. Miller Edwards,
  • Victor Pambuccian

摘要

Tarski’s language for plane absolute geometry has points, equidistance, and betweenness as the only primitive notions. We present an axiom system for plane absolute geometry in Tarski’s language that takes Euclid’s Fourth Postulate as an axiom, but has no congruence axioms of the Side-Angle-Side type for arbitrary triangles. The axiom system presented here validates a statement made by Beppo Levi in 1947.