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1 2003

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The axiom system of similarity geometry : the problem of independency of axioms

Waligóra B.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2003

Vol. 2, nr 1

191--202

There are the axiomatics of the central geometry of similarities in papers [2], [3] and [4]. The primitive notions of these axiomatics are the set E, the distinguished point O, the operation of the addition of points and the quaternary relation of similarity P. The paper [2] contains an axiom system of 2-dimensional geometry. The paper [3] contains an axiom system of the central geometry of similarities for dimensions > 2. These axiomatics have been studying in order to attain the solution to the problem of independency of the axioms. This paper contains the models of independence for some axioms and the proofs of dependence for another axioms. This paper contains plain form of some axioms too.