Splitting the pasch axiom

Victor Pambuccian

doi:10.1007/BF01222689

Splitting the pasch axiom

Victor Pambuccian

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

On the basis of the theory ε^- of Pasch-free 2-dimensional geometry, Pasch's axiom is shown to be equivalent to the conjunction of the following two axioms: "In any right triangle the hypotenuse is greater than the leg" and "If ∠AOB is right, B lies between O and C, and D is the footpoint of the perpendicular from B to AC, then the segment OA is greater than the segment BD." This represents an attempt to split the Pasch axiom with respect to ε^-. Only the question whether the second of the above two axioms is really weaker than Pasch's axiom, remains open.

Original language	English (US)
Pages (from-to)	126-130
Number of pages	5
Journal	Journal of Geometry
Volume	56
Issue number	1-2
DOIs	https://doi.org/10.1007/BF01222689
State	Published - Jan 1 1996

ASJC Scopus subject areas

Geometry and Topology

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10.1007/BF01222689

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AB - On the basis of the theory ε- of Pasch-free 2-dimensional geometry, Pasch's axiom is shown to be equivalent to the conjunction of the following two axioms: "In any right triangle the hypotenuse is greater than the leg" and "If ∠AOB is right, B lies between O and C, and D is the footpoint of the perpendicular from B to AC, then the segment OA is greater than the segment BD." This represents an attempt to split the Pasch axiom with respect to ε-. Only the question whether the second of the above two axioms is really weaker than Pasch's axiom, remains open.

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Splitting the pasch axiom

Abstract

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