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On the computational content of the Bolzano-Weierstraß Principle

✍ Scribed by Pavol Safarik; Ulrich Kohlenbach

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
299 KB
Volume
56
Category
Article
ISSN
0044-3050

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✦ Synopsis

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 i∈N [-ki, ki] (with the standard product metric). This results in optimal program and bound extraction theorems for proofs based on fixed instances of BW, i.e. for BW applied to fixed sequences in i∈N [-ki, ki].

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