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Constructive Axiomatizations of Plane Absolute, Euclidean and Hyperbolic Geometry
Author(s) -
Pambuccian Victor
Publication year - 2001
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/1521-3870(200101)47:1<129::aid-malq129>3.0.co;2-b
Subject(s) - mathematics , non euclidean geometry , constructive , euclidean geometry , hyperbolic geometry , absolute geometry , absolute (philosophy) , hyperbolic triangle , foundations of geometry , geometry , plane (geometry) , ordered geometry , pure mathematics , projective geometry , algebraic geometry , epistemology , computer science , philosophy , convex set , process (computing) , convex optimization , regular polygon , operating system
In this paper we provide quantifier‐free, constructive axiomatizations for 2‐dimensional absolute, Euclidean, and hyperbolic geometry. The main novelty consists in the first‐order languages in which the axiom systems are formulated.