An Analogy between Cardinal Characteristics and Highness Properties of Oracles
An Analogy between Cardinal Characteristics and Highness Properties of Oracles
复制标题
神谕的基本特征与殿下属性的类比
DOI：
10.1142/9789814678001_0001
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Brendle J
中科院分区：
文献类型：
--
作者：
Brendle J
我们提出了一个比喻之间的基数特征集理论和可计算性理论，它指定了一个意义上的图灵预言机是计算强。虽然Rupprecht首先明确研究了这个类比（有效对应于Cichoeli图中的基本特征，博士论文，密歇根大学，2010年），但许多先前的结果可以从这个角度来看。在全面调查的相似性的特征，从Chichoeli的图，我们将其扩展到库尔茨随机性和模拟的Specker-Eda数。
We present an analogy between cardinal characteristics from set theory and highness properties from computability theory, which specify a sense in which a Turing oracle is computationally strong. While this analogy was first studied explicitly by Rupprecht (Effective correspondents to cardinal characteristics in Cichoń's diagram, PhD thesis, University of Michigan, 2010), many prior results can be viewed from this perspective. After a comprehensive survey of the analogy for characteristics from Cichoń's diagram, we extend it to Kurtz randomness and the analogue of the Specker-Eda number.