An Analogy between Cardinal Characteristics and Highness Properties of Oracles
Jörg Brendle, Andrew D. Brooke-Taylor, Keng Meng Ng, André Nies · 2015
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 in his PhD thesis, many prior results can be viewed from this perspective. After a comprehensive survey of the analogy for characteristics from Cichon's diagram, we extend it to Kurtz randomness and the analogue of the Specker-Eda number.