A Reverse Analysis of the Sylvester-Gallai Theorem
Victor Pambuccian
Source: Notre Dame J. Formal Logic Volume 50, Number 3
(2009), 245-260.
Abstract
Reverse analyses of three proofs of the Sylvester-Gallai theorem lead to three different and incompatible axiom systems. In particular, we show that proofs respecting the purity of the method, using only notions considered to be part of the statement of the theorem to be proved, are not always the simplest, as they may require axioms which proofs using extraneous predicates do not rely upon.
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Keywords: reverse analysis; Sylvester-Gallai theorem; projective geometry; Pasch axiom; generalized metric spaces
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1257862037
Digital Object Identifier: doi:10.1215/00294527-2009-010
Zentralblatt MATH identifier: 05657218
Mathematical Reviews number (MathSciNet): MR2572973
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