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Hilbert's Axiom System
They are a set of 20 axioms in David Hilbert's book Grundlagen der Geometrie, for a more modern treatment of Euclidean Geometry.
Hilbert's axiom system is constructed with six primitive notions: three primitive terms:
- Point
- Line
- Plane
and three primitive relations:
- Betweenness: a ternary relation linking points
- Lies on (Containment): three binary relations - one linking points and straight lines, one linking points and planes, and one linking straight lines and planes
- Congruence: two binary relations - one linking line segments and one linking angles, each denoted by an infix ≅.