David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Studia Logica 77 (3):385 - 411 (2004)
We provide a quantifier-free axiom system for plane hyperbolic geometry in a language containing only absolute geometrically meaningful ternary operations (in the sense that they have the same interpretation in Euclidean geometry as well). Each axiom contains at most 4 variables. It is known that there is no axiom system for plane hyperbolic consisting of only prenex 3-variable axioms. Changing one of the axioms, one obtains an axiom system for plane Euclidean geometry, expressed in the same language, all of whose axioms are also at most 4-variable universal sentences. We also provide an axiom system for plane hyperbolic geometry in Tarski's language L B which might be the simplest possible one in that language.
|Keywords||Philosophy Logic Mathematical Logic and Foundations Computational Linguistics|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Marco Aiello, Guram Bezhanishvili, Isabelle Bloch & Valentin Goranko (2012). Logic for Physical Space. Synthese 186 (3):619-632.
Victor Pambuccian (2011). The Simplest Axiom System for Plane Hyperbolic Geometry Revisited. Studia Logica 97 (3):347 - 349.
Similar books and articles
Louis Narens (1974). Measurement Without Archimedean Axioms. Philosophy of Science 41 (4):374-393.
Harvey Friedman (2000). Does Mathematics Need New Axioms? Bulletin of Symbolic Logic 6 (4):401 - 446.
Hajnal Andréka, Judit X. Madarász, István Németi & Gergely Székely, A Logic Road From Special to General Relativity.
Othman Qasim Malhas (1987). Quantum Logic and the Classical Propositional Calculus. Journal of Symbolic Logic 52 (3):834-841.
Patrick Suppes (2000). Quantifier-Free Axioms for Constructive Affine Plane Geometry. Synthese 125 (1-2):263-281.
Ian Pratt & Dominik Schoop (1998). A Complete Axiom System for Polygonal Mereotopology of the Real Plane. Journal of Philosophical Logic 27 (6):621-658.
Brent Mundy (1986). Optical Axiomatization of Minkowski Space-Time Geometry. Philosophy of Science 53 (1):1-30.
Alfred Tarski & Steven Givant (1999). Tarski's System of Geometry. Bulletin of Symbolic Logic 5 (2):175-214.
Added to index2009-01-28
Total downloads9 ( #173,767 of 1,410,217 )
Recent downloads (6 months)1 ( #155,456 of 1,410,217 )
How can I increase my downloads?