### Abstract

We prove that, building upon the universal-existential orthogonality-based axiom system for metric planes presented in [28], one can provide universal-existential axiom systems - expressed solely in terms of the ternary predicate I, with I(abc) standing for 'ab is congruent to ac', which Pieri has introduced 100 years ago - for metric planes, for absolute geometry with the circle axiom, for Euclidean planes, for Euclidean geometry with the circle axiom, for Klingenberg's generalized hyperbolic planes, for plane elementary hyperbolic geometry, as well as for all the finite-dimensional versions of these geometries.

Original language | English (US) |
---|---|

Pages (from-to) | 327-339 |

Number of pages | 13 |

Journal | Rendiconti del Seminario Matematico |

Volume | 67 |

Issue number | 3 |

State | Published - 2009 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Universal-existential axiom systems for geometries expressed with Pieri's isosceles triangle as single primitive notion.** / Pambuccian, Victor.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Universal-existential axiom systems for geometries expressed with Pieri's isosceles triangle as single primitive notion

AU - Pambuccian, Victor

PY - 2009

Y1 - 2009

N2 - We prove that, building upon the universal-existential orthogonality-based axiom system for metric planes presented in [28], one can provide universal-existential axiom systems - expressed solely in terms of the ternary predicate I, with I(abc) standing for 'ab is congruent to ac', which Pieri has introduced 100 years ago - for metric planes, for absolute geometry with the circle axiom, for Euclidean planes, for Euclidean geometry with the circle axiom, for Klingenberg's generalized hyperbolic planes, for plane elementary hyperbolic geometry, as well as for all the finite-dimensional versions of these geometries.

AB - We prove that, building upon the universal-existential orthogonality-based axiom system for metric planes presented in [28], one can provide universal-existential axiom systems - expressed solely in terms of the ternary predicate I, with I(abc) standing for 'ab is congruent to ac', which Pieri has introduced 100 years ago - for metric planes, for absolute geometry with the circle axiom, for Euclidean planes, for Euclidean geometry with the circle axiom, for Klingenberg's generalized hyperbolic planes, for plane elementary hyperbolic geometry, as well as for all the finite-dimensional versions of these geometries.

UR - http://www.scopus.com/inward/record.url?scp=76249124358&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=76249124358&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:76249124358

VL - 67

SP - 327

EP - 339

JO - Rendiconti del Seminario Matematico

JF - Rendiconti del Seminario Matematico

SN - 0373-1243

IS - 3

ER -