一句话：研究 Borel 分段连续函数的细粒度层级，并据此分离集合值函数均匀化问题及 Weihrauch 格中的非构造性原则。
本文研究 Borel 分段连续函数之间细粒度层级，特别是闭分段连续与 G_delta 分段连续之间的间隙。作者旨在厘清可计算性理论中的优先法论证与 G_delta 分段连续概念之间的联系，并利用这一联系考察具有紧图的集合值函数上的均匀化问题。主要结果是在 G_delta 分段连续归约的子类之间得到分离，从而给出均匀化问题的不可归约性证据。该方法还可迁移到 Weihrauch 格，用于分离多种非构造性原则。
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.
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@article{Kihara16,
title = {Borel-Piecewise Continuous Reducibility for Uniformization Problems},
author = {Takayuki Kihara},
journal = {Logical Methods in Computer Science},
volume = {12},
number = {4},
year = {2017},
doi = {10.2168/lmcs-12(4:4)2016}
}