Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990 Association of Mizar Users

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


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

The terminology and notation used in this paper have been introduced in the following articles [1] [2]

Contents (PDF format)


[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.

Received May 16, 1990

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