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Aristotle's axiom in the foundations of geometry |
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| Authors: | Marvin Jay Greenberg |
| Affiliation: | (1) Applied Sciences, University of California, 95064 Santa Cruz, CA, USA |
| Abstract: | In the foundations of non-Euclidean geometry without Dedekind's axiom, Archimedes' axiom suffices to insure that the geometry is hyperbolic, but this axiom is not necessary. The weaker axiom of Aristotle is necessary and sufficient; it uses only geometric variables, not integer variables. |
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