Axiomatizations of hyperbolic geometry: A comparison based on language and quantifier type complexity
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Synthese 133 (3):331 - 341 (2002)
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.
|Keywords||Philosophy Philosophy Epistemology Logic Metaphysics Philosophy of Language|
|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
No citations found.
Similar books and articles
John L. Bell, Two Approaches to Modelling the Universe: Synthetic Differential Geometry and Frame-Valued Sets.
Ludomir Newelski (1999). Geometry of *-Finite Types. Journal of Symbolic Logic 64 (4):1375-1395.
Alfred Tarski & Steven Givant (1999). Tarski's System of Geometry. Bulletin of Symbolic Logic 5 (2):175-214.
L. Kvasz (2011). Kant's Philosophy of Geometry--On the Road to a Final Assessment. Philosophia Mathematica 19 (2):139-166.
Brent Mundy (1986). Optical Axiomatization of Minkowski Space-Time Geometry. Philosophy of Science 53 (1):1-30.
Davide Rizza (2009). Abstraction and Intuition in Peano's Axiomatizations of Geometry. History and Philosophy of Logic 30 (4):349-368.
Jan von Plato (1997). Formalization of Hilbert's Geometry of Incidence and Parallelism. Synthese 110 (1):127-141.
Jan Platvono (1997). Formalization of Hilbert's Geometry of Incidence and Parallelism. Synthese 110 (1):127-141.
Victor Pambuccian (2005). Correction to “Axiomatizations of Hyperbolic Geometry”. Synthese 145 (3):497 -.
Victor Pambuccian (2004). The Simplest Axiom System for Plane Hyperbolic Geometry. Studia Logica 77 (3):385 - 411.
Added to index2009-01-28
Total downloads11 ( #192,359 of 1,696,306 )
Recent downloads (6 months)3 ( #177,943 of 1,696,306 )
How can I increase my downloads?