单纯集、双色图与模糊集上的Lawvere-Tierney拓扑刻画

Lawvere-Tierney topologies for computability theorists

In this article, we introduce certain kinds of computable reduction games with imperfect information. One can view such a game as an extension of the notion of Turing reduction, and generalized Weihrauch reduction as well. Based on the work by Lee and van Oosten, we utilize these games for providing a concrete description of the lattice of the Lawvere-Tierney topologies on the effective topos (equivalently, the subtoposes of the effective topos preordered by geometric inclusion). As an application, for instance, we show that there exists no minimal Lawvere-Tierney topology which is strictly ab…

具效应的拓扑与它们的劳夫-蒂尔尼拓扑

Effectful Toposes and Their Lawvere-Tierney Topologies

本文研究了具效应拓扑及其劳夫-蒂尔尼拓扑，展示了双否定拓扑的sheaf拓扑与延续传递风格效果拓扑的同构性，为经典可实现性提供了模型。

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。