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.
- Inner form of the Pasch axiom
- Plane ordered geometry
- Weakly ordered plane
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