The Simplest Axiom System for Plane Hyperbolic Geometry Revisited

Victor Pambuccian

doi:10.1007/s11225-011-9314-6

The Simplest Axiom System for Plane Hyperbolic Geometry Revisited

Victor Pambuccian

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

4 Scopus citations

Abstract

Using the axiom system provided by Carsten Augat in [1], it is shown that the only 6-variable statement among the axioms of the axiom system for plane hyperbolic geometry (in Tarski's language L_B≡), we had provided in [3], is superfluous. The resulting axiom system is the simplest possible one, in the sense that each axiom is a statement in prenex form about at most 5 points, and there is no axiom system consisting entirely of at most 4-variable statements.

Original language	English (US)
Pages (from-to)	347-349
Number of pages	3
Journal	Studia Logica
Volume	97
Issue number	3
DOIs	https://doi.org/10.1007/s11225-011-9314-6
State	Published - Apr 1 2011

Keywords

Euclidean geometry
Hyperbolic geometry
axiom system
betweenness and equidistance
simplicity

ASJC Scopus subject areas

Logic
History and Philosophy of Science

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10.1007/s11225-011-9314-6

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KW - Hyperbolic geometry

KW - axiom system

KW - betweenness and equidistance

KW - simplicity

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The Simplest Axiom System for Plane Hyperbolic Geometry Revisited

Abstract

Keywords

ASJC Scopus subject areas

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