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axiom system; Euclidean geometry; projective space; elliptic plane; formally real pythagorean field
We present an axiom system for class of full Euclidean spaces (i.e. of projective closures of Euclidean spaces) and prove the representation theorem for our system, using connections between Euclidean spaces and elliptic planes.
[1] M. Kordos: Elements of projective and projective-metric geometry. (Polish). PAN Warszawa (1984), 131.
[2] M. Kordos: Elliptic geometry as a theory of one binary relation. Bull. PAN. vol. XXI, No. 7 (1973). MR 0333927 | Zbl 0267.50002
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