| Title: | Weak weak König's lemma in constructive reverse mathematics |
| DOI No: | 10.1142/9789814293020_0010 |
| Source: | PROCEEDINGS OF THE 10TH ASIAN LOGIC CONFERENCE (pp 263-270)
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| Author(s): | Takako Nemoto
www.math.tohoku.ac.jp/~sa4m20/ Mathematical Institute, Tohoku University, Sendai, 980-8578, Japan
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| Abstract: | In this paper we show in a constructive setting that weak weak König's lemma, the assertion that every binary tree T ⊆ {-1,1}<ℕ without infinite paths satisfies limn→∞ ♯{t ∈ T : length(t) = n}/2n = 0, is equivalent to the following assertion: Every positive uniformly continuous function f : [0,1] → ℝ satisfies limδ→0µ({x ∈ [0,1] : f(x) < δ}) = 0. |
| Keywords: | constructive reverse mathematics; Brouwer's fan theorem; weak weak König's lemma; uniform continuous function
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