Notre Dame Journal of Formal Logic

A Reverse Analysis of the Sylvester-Gallai Theorem

Victor Pambuccian

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.

Article information

Source
Notre Dame J. Formal Logic Volume 50, Number 3 (2009), 245-260.

Dates
First available in Project Euclid: 10 November 2009

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

Subjects
Primary: 03C62: Models of arithmetic and set theory [See also 03Hxx]
Secondary: 03B30: Foundations of classical theories (including reverse mathematics) [See also 03F35] 11A05: Multiplicative structure; Euclidean algorithm; greatest common divisors

Keywords
reverse analysis Sylvester-Gallai theorem projective geometry Pasch axiom generalized metric spaces

Citation

Pambuccian, Victor. A Reverse Analysis of the Sylvester-Gallai Theorem. Notre Dame Journal of Formal Logic 50 (2009), no. 3, 245--260. doi:10.1215/00294527-2009-010. http://projecteuclid.org/euclid.ndjfl/1257862037.


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