### Abstract

We provide a universal axiom system for plane hyperbolic geometry in a first-order language with two sorts of individual variables, 'points' (upper-case) and 'lines' (lower-case), containing three individual constants, A_{0}, A_{1}, A_{2}, standing for three non-collinear points, two binary operation symbols, φ and ι, with φ(A, B) = ι to be interpreted as 'ι is the line joining A and B' (provided that A ≠ B, an arbitrary line, otherwise), and ι(g, h) = P to be interpreted as 'P is the point of intersection of g and h (provided that g and h are distinct and have a point of intersection, an arbitrary point, otherwise), and two binary operation symbols, π_{1}(P, ι) and π_{2}(P, ι), with π_{i}(P, ι) = g (for i = 1, 2) to be interpreted as 'g is one of the two limiting parallel lines from P to ι (provided that P is not on ι, an arbitrary line, otherwise).

Original language | English (US) |
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Pages (from-to) | 475-488 |

Number of pages | 14 |

Journal | Mathematical Logic Quarterly |

Volume | 47 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 2001 |

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### Keywords

- Constructive axiomatization
- Hyperbolic geometry

### ASJC Scopus subject areas

- Logic