## 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 theorem

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.

Volume: Volume 10, Issue 4
Published on: December 24, 2014
Accepted on: June 25, 2015
Submitted on: November 6, 2013
Keywords: Mathematics - Logic,Computer Science - Logic in Computer Science