More reverse mathematics of the Heine-Borel Theorem

被引：0

作者：

Hirst, Jeffry L. ^{[1
]}

Miller, Jessica ^{[2
]}

机构：

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

[2] Catawba Valley Community Coll, Dept Math, 2550 US Highway 70 SE, Hickory, NC 28602 USA

来源：

JOURNAL OF LOGIC AND ANALYSIS | 2012年 / 4卷

关键词：

reverse mathematics; Heine-Borel; compact; countable closed; derived sequence; rca; wkl; aca; atr;

D O I：

10.4115/jla.2012.4.6

中图分类号：

B81 [逻辑学（论理学）];

学科分类号：

010104 ; 010105 ;

摘要：

Using the techniques of reverse mathematics, we characterize subsets X subset of [0,1] in terms of the strength of HB(X), the Heine-Borel Theorem for the subset. We introduce W(X), formalizing the notion that the Heine-Borel Theorem for X is weak, and S(X), formalizing the notion that the theorem is strong. Using these, we can prove the following three results: RCA(0) proves W(X) -> HB(X), RCA(0) proves S(X) -> (HB(X) -> WKL0), and ATR(0) proves (X) over bar exists -> (W(X) V S(X)).

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页数：10

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