### Abstract

In this paper we provide quantifier‐free, constructive axiomatizations for several fragments of plane Euclidean geometry over Euclidean fields, such that each axiom contains at most 4 variables. The languages in which they are expressed contain only at most ternary operations. In some precisely defined sense these axiomatizations are the simplest possible.

Original language | English (US) |
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Pages (from-to) | 384-394 |

Number of pages | 11 |

Journal | Mathematical Logic Quarterly |

Volume | 41 |

Issue number | 3 |

DOIs | |

State | Published - 1995 |

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### Keywords

- Cartesian Plane
- Constructive axiomatization
- Euclidean Plane
- Ordered Euclidean Plane
- Plane Euclidean geometry

### ASJC Scopus subject areas

- Logic