A Reverse Analysis of the Sylvester-Gallai Theorem

被引：9

作者：

Pambuccian, Victor ^{[1
]}

机构：

[1] Arizona State Univ W Campus, New Sch Interdisciplinary Arts & Sci, Phoenix, AZ 85069 USA

来源：

NOTRE DAME JOURNAL OF FORMAL LOGIC | 2009年 / 50卷 / 03期

关键词：

reverse analysis; Sylvester-Gallai theorem; projective geometry; Pasch axiom; generalized metric spaces;

D O I：

10.1215/00294527-2009-010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：245 / 260

页数：16

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