Weakly ordered plane geometry |
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Authors: | Victor Pambuccian |
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Institution: | (1) University of Colorado at Colorado Springs, Colorado Springs, CO 80918, USA |
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Abstract: | A plane geometry is introduced, which although ordered such that both every line is densely linearly ordered without first
or last element and such that every line partitions the points of the plane not incident with it into two convex half-planes,
does not need to satisfy the Pasch axiom. An alternate axiomatization of ordered planes is obtained by adding several axioms,
including the inner form of the Pasch axiom. The missing link between the inner form of Pasch’s axiom and the full Pasch axiom
is herewith determined. |
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Keywords: | |
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