Weak weak Konig's lemma in constructive reverse mathematics

被引：3

作者：

Nemoto, Takako ^{[1
]}

机构：

[1] Tohoku Univ, Math Inst, Sendai, Miyagi 9808578, Japan

来源：

PROCEEDINGS OF THE 10TH ASIAN LOGIC CONFERENCE | 2010年

关键词：

constructive reverse mathematics; Brouwer's fan theorem; weak weak Konig's lemma; uniform continuous function;

D O I：

10.1142/9789814293020_0010

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper we show in a constructive setting that weak weak Konig's lemma, the assertion that every binary tree T subset of {-1, 1}(<N) without infinite paths satisfies lim(n ->infinity) #{t is an element of T : length(t) = n}/2(n) = 0, is equivalent to the following assertion: Every positive uniformly continuous function f : [0,1] -> R satisfies lim(delta -> 0) mu({x is an element of [0, 1] : f (x) < delta}) = 0.

引用

页码：263 / 270

页数：8