  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
Cicho\'{n}'s diagram.
