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Axiomatizations of hyperbolic geometry

a comparison based on language and quantifier type complexity

Victor Pambuccian

pp. 331-341

Abstrakt

Hyperbolic geometry can be axiomatized using the notions of order andcongruence (as in Euclidean geometry) or using the notion of incidencealone (as in projective geometry). Although the incidence-based axiomatizationmay be considered simpler because it uses the single binary point-linerelation of incidence as a primitive notion, we show that it issyntactically more complex. The incidence-based formulation requires some axioms of the quantifier-type forallexistsforall, while the axiom system based on congruence and order can beformulated using only forallexists-axioms.

Publication details

Published in:

(2002) Synthese 133 (3).

Seiten: 331-341

DOI: 10.1023/A:1021294808742

Referenz:

Pambuccian Victor (2002) „Axiomatizations of hyperbolic geometry: a comparison based on language and quantifier type complexity“. Synthese 133 (3), 331–341.