Classical and Non-classical Pasch Configurations in Ordered Affine Planes

Henryk Oryszczyszyn

Warsaw University, Bialystok

Krzysztof Prazmowski

Warsaw University, Bialystok

Malgorzata Prazmowska

Warsaw University, Bialystok

Summary.

Several configuration axioms, which are commonly called in the literature ``Pasch Axioms" are introduced; three of them were investigated by Szmielew and concern invariantability of the betweenness relation under parallel projections, and two other were introduced by Tarski. It is demonstrated that they all are consequences of the trapezium axiom, adopted to characterize ordered affine spaces.

Supported by RPBP.III-24.C2.

MML Identifier: PASCH

Contents (PDF format)

Bibliography

[1] Henryk Oryszczyszyn and Krzysztof Prazmowski. Analytical ordered affine spaces. Journal of Formalized Mathematics, 2, 1990.

[2] Henryk Oryszczyszyn and Krzysztof Prazmowski. Ordered affine spaces defined in terms of directed parallelity --- part I. Journal of Formalized Mathematics, 2, 1990.