More reverse mathematics of the Heine-Borel Theorem
نویسندگان
چکیده
Using the techniques of reverse mathematics, we characterize subsets X ⊆ [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: RCA0 `W(X)→ HB(X), RCA0 ` S(X)→ (HB(X)→WKL0), and ATR0 ` X exists→ (W(X) ∨ S(X)). 2010 Mathematics Subject Classification 03B30, 03F35 (primary); 03F60, 26E40 (secondary)
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عنوان ژورنال:
- J. Logic & Analysis
دوره 4 شماره
صفحات -
تاریخ انتشار 2012