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An analogy between cardinal characteristics and highness properties of oracles

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.

preprint2014arXivOpen access
Jörg BrendleAndrew Brooke-TaylorKeng Meng NgAndré Nies
math.LO
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Open access4 authors1 topic
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Jörg BrendleAndrew Brooke-TaylorKeng Meng NgAndré Nies

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