修正可实现性子拓扑与全Weihrauch归约
Modified realizability subtoposes and total Weihrauch reducibility
浏览论文内容
中文总结 AI 辅助
该研究在全可计算框架下提出归约概念，利用层子拓扑分离了弱排中律、小有限全知原则与马尔可夫原则等逻辑原则的层级。
中文摘要 AI 辅助
近年来，从Lawvere-Tierney拓扑及其层的角度，关于谕示可计算性的基础研究取得了快速发展。本文在全可计算框架下，提出并分析了归约的概念；随后利用全可计算环境中由谕示导出的层子拓扑，建立了各类逻辑原则层级之间的分离关系，包括弱排中律层级（$\boldsymbol{WLEM}$）、小有限全知原则层级（$\boldsymbol{LLPO}$）与马尔可夫原则（$\boldsymbol{MP}$）的层级分离。
英文摘要
In recent years, there has been rapid development in the foundational study of oracle computability from the perspective of Lawvere-Tierney topologies and their sheaves. In this article, we formulate and analyze the notion of reducibility within the framework of total computability. Then, using sheaf subtoposes derived from oracles in the total computable setting, we establish separations between various hierarchies of logical principles, including the hierarchies of the weak law of excluded middle $\mathbf{WLEM}$, the lessor limited principle of omniscience $\mathbf{LLPO}$, and Markov's principle $\mathbf{MP}$.
