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In our earlier article [12], the first part of axioms of geometry proposed by Alfred Tarski [14] was formally introduced by means of Mizar proof assistant [9]. We defined a structure TarskiPlane with the following predicates: of betweenness between (a ternary relation), of congruence of segments equiv (quarternary relation), which satisfy the following properties: congruence symmetry (A1), congruence equivalence relation (A2), congruence identity (A3), segment construction (A4), SAS (A5), betweenness...
We characterize an important class of generalized projective geometries by the
following essentially equivalent properties: (1) admits a central null-system;
(2) admits inner polarities: (3) is associated to a unital Jordan
algebra. These geometries, called of the first kind, play in the category of generalized
projective geometries a rôle comparable to the one of the projective line in the category
of ordinary projective geometries. In this general set-up, we prove an analogue of von
Staudt’s...
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