论文标题
重新考虑甲骨文的概念：律师拓扑的前传
Rethinking the notion of oracle: A prequel to Lawvere-Tierney topologies for computability theorists
论文作者
论文摘要
我们提出了甲骨文的三种不同观点。首先，甲骨文是黑盒子。其次，甲骨文是改变我们访问数学对象的方式的工具。第三，甲骨文是导致真实价值变化的因素。正式地，第二个观点倡导者是Oracle是编码集类别（保存基础集）类别的内for函数 - 我们将其与通用闭合操作员相关联。第三个观点提倡甲骨文是真实价值观对象的操作 - 我们将其与律师 - 蒂尔尼拓扑结合起来。这三个观点在这三个领域，计算理论，综合描述集理论和有效的拓扑理论之间建立了联系。
We present three different perspectives of oracle. First, an oracle is a blackbox; second, an oracle is a tool to change the way we access mathematical objects; and third, an oracle is a factor that causes a change in truth values. Formally, the second perspective advocates that an oracle is an endofunctor on the category of coded sets (preserving underlying sets) -- we associate it with a universal closure operator. The third perspective advocates that an oracle is an operation on the object of truth values -- we associate it with a Lawvere-Tierney topology. These three perspectives create a link between the three fields, computability theory, synthetic descriptive set theory, and effective topos theory.
