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keywords<br />
abstract<br />
plane geometry, axiomatic system, axiom, undefined term, interpretation,<br />
model<br />
An axiomatic system is an organized logical structure consisting of undefined<br />
terms, axioms, defined terms, a system of inference rules and theorems. A<br />
model for an axiomatic system is an interpretation of this system, consisting of<br />
the attribution of particular meanings to the undefined terms, in order that the<br />
axioms, read in the light of this interpretation, become true propositions.<br />
In this work we will present plane geometries, from abstract to neutral or<br />
absolute geometries. We will make a brief reference to Euclidean and<br />
hyperbolic plane geometries, whose axiomatic systems are categorical. Finally,<br />
we will present the real cartesian plane and Poincaré half plane as models for<br />
the Euclidean and hyperbolic geometries, respectively.