Axiomatizations of hyperbolic geometry: A comparison based on language and quantifier type complexity

Synthese 133 (3):331 - 341 (2002)
Abstract
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)
Reprint years 2004
DOI 10.1023/A:1021294808742
Options
 Save to my reading list
Follow the author(s)
Edit this record
My bibliography
Export citation
Find it on Scholar
Mark as duplicate
Request removal from index
Revision history
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 31,317
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA

Add more citations

Similar books and articles
Added to PP index
2009-01-28

Total downloads
29 ( #198,359 of 2,223,771 )

Recent downloads (6 months)
3 ( #180,515 of 2,223,771 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature