可计算性理论家的Lawvere-Tierney拓扑
Lawvere-Tierney topologies for computability theorists
摘要：
在这篇文章中，我们介绍了某些类型的不完全信息可计算约简博弈。人们可以把这样的博弈看作是图灵归约概念的延伸，也可以看作是广义Weihrauch归约概念的延伸。在Lee和van Oosten工作的基础上，我们利用这些博弈对有效拓扑（等价地，有效拓扑的子拓扑由几何包含预排序）上的Lawvere-Tierney拓扑的格提供了一个具体的描述.作为一个应用，例如，我们证明了不存在严格高于有效拓扑上的单位拓扑的最小Lawvere-Tierney拓扑。
英文摘要：
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 above the identity topology on the effective topos.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
