We prove that, building upon the universal-existential orthogonality-based axiom system for metric planes presented in , 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)|
|Number of pages||13|
|Journal||Rendiconti del Seminario Matematico|
|State||Published - Dec 1 2009|
ASJC Scopus subject areas