## Kihara, Takayuki - Borel-piecewise continuous reducibility for uniformization problems

lmcs:2173 - Logical Methods in Computer Science, October 18, 2016, Volume 12, Issue 4
Borel-piecewise continuous reducibility for uniformization problems

Authors: Kihara, Takayuki

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.

Source : oai:arXiv.org:1608.03269
DOI : 10.2168/LMCS-12(4:4)2016
Volume: Volume 12, Issue 4
Published on: October 18, 2016
Submitted on: October 18, 2016
Keywords: Mathematics - Logic,Computer Science - Logic in Computer Science