Pasch's Axiom in Euclidean Geometry
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Tarski axiomatized Euclidean plane geometry in first-order logic using two primitive relations: the formula means "
lies between
and
", while
means "
is as distant from
as
is from
". Using
, Pasch's axiom has the form
Contributed by: Izidor Hafner (April 2018)
Open content licensed under CC BY-NC-SA
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Reference
[1] A. Tarski, "What Is Elementary Geometry?" The Axiomatic Method with Special Reference to Geometry and Physics (L. Henkin, P. Suppes and A. Tarski, eds.), Amsterdam: North-Holland Publishing Company, 1959, pp. 16–29.
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