### Abstract

We provide a collinearity based elementary axiomatics of optimal quantifier complexity ∀∃∀∃ for the geometry inside a triangle and reprove that collinearity cannot be defined in terms of segment congruence, the metric being Hilbert's projective metric.

Original language | English (US) |
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Pages (from-to) | 165-175 |

Number of pages | 11 |

Journal | Beitrage zur Algebra und Geometrie |

Volume | 49 |

Issue number | 1 |

State | Published - Apr 7 2008 |

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### Keywords

- Collinearity
- Hilbert geometry inside a triangle
- Quantifier complexity
- Segment congruence

### ASJC Scopus subject areas

- Algebra and Number Theory
- Geometry and Topology