Transfinite sequences of topologies, descriptive complexity, and approximating equivalence relations

Ideal Topologies in Higher Descriptive Set Theory

We investigate generalizations of the topology of the higher Cantor space on $2^κ$, based on arbitrary ideals rather than the bounded ideal on $κ$. Our main focus is on the topology induced by the nonstationary ideal, and we call this topology the nonstationary topology, or also the Edinburgh topology on $2^κ$. It may be of independent interest that as a side result, we show $κ$-Silver forcing to satisfy a strong form of Axiom $A$ not only if $κ$ is inaccessible (which is well-known), but also under the assumption $\diamondsuit_κ$.

$κ$-Borel集、$κ$-Baire空间与拓扑之间的滤过

$κ$-Borel sets, $κ$-Baire spaces, and filtrations between topologies

该研究聚焦拓扑间插值的滤过结构，证明了滤过稳定于更强拓扑的一般性结果，揭示了$κ$-Borel集与$κ$-Baire性在拓扑滤过研究中的关联作用。

重思oracle（谕示）的概念：面向可计算性理论研究者的Lawvere-Tierney拓扑学前篇

Rethinking the notion of oracle: A prequel to Lawvere-Tierney topologies for computability theorists

该研究提出oracle（谕示）的黑盒、访问方式工具、真值变化因子三种视角，分别对应通用闭包算子与Lawvere-Tierney拓扑，为可计算性等三个领域建立了关联。