There has recently been work by multiple groups in extracting the properties associated with cardinal invariants of the continuum and translating these properties into similar analogous combinatorial properties of computational oracles. Each property yields a highness notion in the Turing degrees. In this paper we study the highness notions that result from the translation of the evasion number and its dual, the prediction number, as well as two versions of the rearrangement number. When translated appropriately, these yield four new highness notions. We will define these new notions, show some of their basic properties and place them in the computability-theoretic version of Cichoń's diagram.

最近，多个小组开展了一些工作，以提取与连续体的基本不变式相关的属性，并将这些属性转换为类似的计算oracle组合属性。每个属性都产生图灵度的高级概念。在本文中，我们研究了逃避数及其对偶数，预测数以及两个重排数形式的转换所产生的高度概念。适当翻译后，这些将产生四个新的高级概念。我们将定义这些新概念，展示它们的一些基本属性，并将它们放在Cichoń图的可计算性理论版本中。