A Reverse analysis of the Sylvester-Gallai theorem

Victor Pambuccian

doi:10.1215/00294527-2009-010

A Reverse analysis of the Sylvester-Gallai theorem

Victor Pambuccian

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

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.

Original language	English (US)
Pages (from-to)	245-260
Number of pages	16
Journal	Notre Dame Journal of Formal Logic
Volume	50
Issue number	3
DOIs	https://doi.org/10.1215/00294527-2009-010
State	Published - 2009

Keywords

Generalized metric spaces
Pasch axiom
Projective geometry
Reverse analysis
Sylvester-Gallai theorem

ASJC Scopus subject areas

Logic

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10.1215/00294527-2009-010

Cite this

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AB - 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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KW - Projective geometry

KW - Reverse analysis

KW - Sylvester-Gallai theorem

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A Reverse analysis of the Sylvester-Gallai theorem

Abstract

Keywords

ASJC Scopus subject areas

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