An analogy between cardinal characteristics and highness properties of oracles
Brendle, Jörg · Brooke-Taylor, Andrew · Ng, Keng Meng · Nies, André
Original · EN
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.
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