| 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. |
