### 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 | |

State | Published - Apr 2011 |

### Fingerprint

### Keywords

- axiom system
- betweenness and equidistance
- Euclidean geometry
- Hyperbolic geometry
- simplicity

### ASJC Scopus subject areas

- Logic

### Cite this

**The Simplest Axiom System for Plane Hyperbolic Geometry Revisited.** / Pambuccian, Victor.

Research output: Contribution to journal › Article

*Studia Logica*, vol. 97, no. 3, pp. 347-349. https://doi.org/10.1007/s11225-011-9314-6

}

TY - JOUR

T1 - The Simplest Axiom System for Plane Hyperbolic Geometry Revisited

AU - Pambuccian, Victor

PY - 2011/4

Y1 - 2011/4

N2 - 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 LB≡), 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.

AB - 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 LB≡), 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.

KW - axiom system

KW - betweenness and equidistance

KW - Euclidean geometry

KW - Hyperbolic geometry

KW - simplicity

UR - http://www.scopus.com/inward/record.url?scp=79953779804&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79953779804&partnerID=8YFLogxK

U2 - 10.1007/s11225-011-9314-6

DO - 10.1007/s11225-011-9314-6

M3 - Article

AN - SCOPUS:79953779804

VL - 97

SP - 347

EP - 349

JO - Studia Logica

JF - Studia Logica

SN - 0039-3215

IS - 3

ER -