TY - JOUR

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

AU - Pambuccian, Victor

PY - 2009/12/1

Y1 - 2009/12/1

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.

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

M3 - Article

AN - SCOPUS:76249124358

SN - 0373-1243

VL - 67

SP - 327

EP - 339

JO - Rendiconti del Seminario Matematico

JF - Rendiconti del Seminario Matematico

IS - 3

ER -