A Reverse analysis of the Sylvester-Gallai theorem

Research output: Contribution to journalArticle

7 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 languageEnglish (US)
Pages (from-to)245-260
Number of pages16
JournalNotre Dame Journal of Formal Logic
Volume50
Issue number3
DOIs
StatePublished - Dec 1 2009

Keywords

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

ASJC Scopus subject areas

  • Logic

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