Bounded variation and the strength of Helly's selection theorem

Alexander P. Kreuzer

doi:10.2168/LMCS-10(4:16)2014

Alexander P. Kreuzer - Bounded variation and the strength of Helly's selection theorem

lmcs:980 - Logical Methods in Computer Science, December 24, 2014, Volume 10, Issue 4 - https://doi.org/10.2168/LMCS-10(4:16)2014

Bounded variation and the strength of Helly's selection theoremArticle

Authors: Alexander P. Kreuzer

We analyze the strength of Helly's selection theorem HST, which is the most important compactness theorem on the space of functions of bounded variation. For this we utilize a new representation of this space intermediate between $L_1$ and the Sobolev space W1,1, compatible with the, so called, weak* topology. We obtain that HST is instance-wise equivalent to the Bolzano-Weierstra\ss\ principle over RCA0. With this HST is equivalent to ACA0 over RCA0. A similar classification is obtained in the Weihrauch lattice.

https://doi.org/10.2168/LMCS-10(4:16)2014

Source: arXiv.org:1308.3881

Volume: Volume 10, Issue 4

Published on: December 24, 2014

Imported on: November 6, 2013

Keywords: Mathematics - Logic,Computer Science - Logic in Computer Science

Licence: arXiv.org - Non-exclusive license to distribute