An analogy between cardinal characteristics and highness properties of oracles
Logic
2014-09-26 v2
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.
Keywords
Cite
@article{arxiv.1404.2839,
title = {An analogy between cardinal characteristics and highness properties of oracles},
author = {Jörg Brendle and Andrew Brooke-Taylor and Keng Meng Ng and André Nies},
journal= {arXiv preprint arXiv:1404.2839},
year = {2014}
}
Comments
28 pages; version 2 post refereeing, in particular with due credit to Rupprecht for results from his thesis of which we were previously unaware