Takayuki Kihara - Borel-piecewise continuous reducibility for uniformization problems

lmcs:2173 - Logical Methods in Computer Science, April 27, 2017, Volume 12, Issue 4 - https://doi.org/10.2168/LMCS-12(4:4)2016
Borel-piecewise continuous reducibility for uniformization problems

Authors: Takayuki Kihara

We study a fine hierarchy of Borel-piecewise continuous functions, especially, between closed-piecewise continuity and $G_\delta$-piecewise continuity. Our aim is to understand how a priority argument in computability theory is connected to the notion of $G_\delta$-piecewise continuity, and then we utilize this connection to obtain separation results on subclasses of $G_\delta$-piecewise continuous reductions for uniformization problems on set-valued functions with compact graphs. This method is also applicable for separating various non-constructive principles in the Weihrauch lattice.

Volume: Volume 12, Issue 4
Published on: April 27, 2017
Accepted on: October 18, 2016
Submitted on: March 19, 2016
Keywords: Mathematics - Logic,Computer Science - Logic in Computer Science


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