Hindman's theorem, ultrafilters. and reverse mathematics

被引：9

作者：

Hirst, JL ^{[1
]}

机构：

[1] Appalachian State Univ, Dept Math Sci, Boone, NC 28608 USA

来源：

JOURNAL OF SYMBOLIC LOGIC | 2004年 / 69卷 / 01期

关键词：

Hindman's theorem; Milliken's theorem; reverse mathematics; computability;

D O I：

10.2178/jsl/1080938825

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Assuming CH. Hindman [2] showed that the existence of certain ultrafilters on the power set of the natural numbers is equivalent to Hindman's Theorem. Adapting this work to a countable setting formalized in RCA(0). this article proves the equivalence of the existence of certain Ultrafilters on countable Boolean algebras and an iterated form of Hindman's Theorem. which is closely related to Milliken's Theorem. A computable restriction of Hindman's Theorem follows as a corollary.

引用

页码：65 / 72

页数：8

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