Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 50, Number 3 (2009), 245-260.
A Reverse Analysis of the Sylvester-Gallai Theorem
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.
Notre Dame J. Formal Logic Volume 50, Number 3 (2009), 245-260.
First available in Project Euclid: 10 November 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
Pambuccian, Victor. A Reverse Analysis of the Sylvester-Gallai Theorem. Notre Dame J. Formal Logic 50 (2009), no. 3, 245--260. doi:10.1215/00294527-2009-010. https://projecteuclid.org/euclid.ndjfl/1257862037.