Constructive axiomatization of non-elliptic metric planes

• Autorzy: Pambuccian V.
• Języki publikacji: EN

Abstrakty

EN

In this paper we provide a quantifier-free, constructive axiomatization for F. Bachmann's non-elliptic metric planes. The language in which it is expressed contains three individual constants, a0, a1, a2, standing for three non-collinear points, and two operation symbols, F and pi. F(abc) is the footpoint of the perpendicular from c to the line ab, if a [does not equal] b, and a itself if a = b, and pi(abc) is the fourth refection point whenever a, b, c are collinear points with a [does not equal] b and b [does not equal] c, and arbitrary otherwise. It is an open problem whether non-elliptic metric planes can be axiomatized by quantifler-free axioms in a language containing a0, a1, a2, F, and the binary operation sigma, where sigma(ab) is the point obtained by reflecting b m a.

Słowa kluczowe

EN

non-elliptic metric planes; constructive axiomatization; quantifier-free axiomatization

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2003
• Tom: Vol. 51, no 1
• Strony: 49--57
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Pambuccian V.

• Department of Integrative Studies, Arizona State University West Phoenix, AZ 85069-7100, U.S.A.

Bibliografia

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