Abstract
In Euclidean geometry and in absolute geometry fragments of the principle of duality hold. Bachmann (Aufbau der Geometrie aus dem Spiegelungsbegriff, 1973, §3.9) posed the problem to find a general theorem which describes the extent of an allowed dualization. It is the aim of this paper to solve this problem. To this end a first-order axiomatization of Euclidean (resp. absolute) geometry is provided which allows the application of Gödel’s Completeness Theorem for first-order logic and the solution of Bachmann’s problem.
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Struve, R. The principle of duality in Euclidean and in absolute geometry. J. Geom. 107, 707–717 (2016). https://doi.org/10.1007/s00022-016-0314-6
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DOI: https://doi.org/10.1007/s00022-016-0314-6