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We will apply the methods developed in the field of ‘proof mining’ to the Bolzano‐Weierstraß theorem BW and calibrate the computational contribution of using this theorem in proofs of combinatorial statements. We provide an explicit solution of the Gödel functional interpretation (combined with negative translation) as well as the monotone functional interpretation of BW for the product space Πi ∈ℕ...
The aim of this paper is to determine the logical and computational strength of instances of the Bolzano‐Weierstraß principle (BW) and a weak variant of it.
We show that BW is instance‐wise equivalent to the weak König’s lemma for Σ01‐trees (Σ01‐ WKL). This means that from every bounded sequence of reals one can compute an infinite Σ01‐0/1‐tree, such that each infinite branch of it yields an accumulation...
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