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arXiv · 1404.2839

An analogy between cardinal characteristics and highness properties of oracles

Jörg Brendle·Andrew Brooke-Taylor·Keng Meng Ng·André Nies
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Abstract

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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Jörg Brendle, Andrew Brooke-Taylor, Keng Meng Ng, André Nies. 2014-09-25. An analogy between cardinal characteristics and highness properties of oracles. https://arxiv.org/abs/1404.2839

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