A Reverse Analysis of the Sylvester-Gallai Theorem
Pambuccian, Victor
Notre Dame J. Formal Logic, Tome 50 (2009) no. 1, p. 245-260 / Harvested from Project Euclid
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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.
Publié le : 2009-07-15
Classification:  reverse analysis,  Sylvester-Gallai theorem,  projective geometry,  Pasch axiom,  generalized metric spaces,  03C62,  03B30,  11A05 
@article{1257862037,
     author = {Pambuccian, Victor},
     title = {A Reverse Analysis of the Sylvester-Gallai Theorem},
     journal = {Notre Dame J. Formal Logic},
     volume = {50},
     number = {1},
     year = {2009},
     pages = { 245-260},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1257862037}
}

Pambuccian, Victor. A Reverse Analysis of the Sylvester-Gallai Theorem. Notre Dame J. Formal Logic, Tome 50 (2009) no. 1, pp.  245-260. http://gdmltest.u-ga.fr/item/1257862037/