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Absolute geometry with the fourth postulate
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DOI：10.1007/s13366-026-00835-z.png)
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Abstract
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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.
Keywords:
Axiom system
Euclid's fourth postulate
Absolute geometry
Alfred Tarski
Journal
B
IF:
0.4
Papers:
38
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0