IS THE MISSING AXIOM OF MATROID THEORY LOST FOREVER?

被引：8

作者：

Mayhew, Dillon ^{[1
]}

Whittle, Geoff ^{[1
]}

Newman, Mike ^{[2
]}

机构：

[1] Victoria Univ Wellington, Sch Math Stat & Operat Res, Wellington, New Zealand

[2] Univ Ottawa, Dept Math & Stat, Ottawa, ON, Canada

来源：

QUARTERLY JOURNAL OF MATHEMATICS | 2014年 / 65卷 / 04期

关键词：

D O I：

10.1093/qmath/hat031

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We conjecture that it is not possible to finitely axiomatize matroid representability in monadic second-order logic (MSOL) for matroids, and we describe some partial progress towards this conjecture. We present a collection of sentences in MSOL and show that it is possible to finitely axiomatize matroids using only sentences in this collection. Moreover, we can also axiomatize representability over any fixed finite field (assuming Rota's conjecture holds). We prove that it is not possible to finitely axiomatize representability, or representability over any fixed infinite field, using sentences from the collection.

引用

页码：1397 / 1415

页数：19

共 14 条

[1]

[Anonymous], 2002, Model Theory: An Introduction, Graduate Texts in Mathematics

[2]

[Anonymous], 2010, Matroid theory

[3]

Flum J org, 2006, SPRINGER MONOGRAPHS, V2nd

[4] Totally free expansions of matroids [J].