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) |
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Pages (from-to) | 245-260 |
Number of pages | 16 |
Journal | Notre Dame Journal of Formal Logic |
Volume | 50 |
Issue number | 3 |
DOIs | |
State | Published - 2009 |
Keywords
- Generalized metric spaces
- Pasch axiom
- Projective geometry
- Reverse analysis
- Sylvester-Gallai theorem
ASJC Scopus subject areas
- Logic