论文标题
可视性限制以理论方法的可计算性限制
Countability constraints in order-theoretic approaches to computability
论文作者
论文摘要
无数套件上的可计算性没有标准形式化，与图灵机给出的可数集不同。在这些集合中定义可计算性的一些方法依赖于订单理论结构将这些概念从图灵机转换为无数的空间。由于这些机器在这些方法中被用作可计算性的基准，因此对有序结构的可数限制是基本的。在这里，我们在计算性的顺序理论理论和一些更常见的有序理论可算可约束中显示了通常的可算置性限制之间的几个关系，例如订单密度属性和订单结构的功能特征在多实量方面。结果，我们展示了如何通过可视性顺序密度和多功能限制以某些顺序结构引入可计算性。
Computability on uncountable sets has no standard formalization, unlike that on countable sets, which is given by Turing machines. Some of the approaches to define computability in these sets rely on order-theoretic structures to translate such notions from Turing machines to uncountable spaces. Since these machines are used as a baseline for computability in these approaches, countability restrictions on the ordered structures are fundamental. Here, we show several relations between the usual countability restrictions in order-theoretic theories of computability and some more common order-theoretic countability constraints, like order density properties and functional characterizations of the order structure in terms of multi-utilities. As a result, we show how computability can be introduced in some order structures via countability order density and multi-utility constraints.
