Cichon's diagram for Turing oracles

Andrew Brooke-Taylor, University of Leeds. Part of the PCC seminar series

Abstract: There is a natural analogy that can be drawn between cardinal characteristics of the continuum and highness properties of Turing oracles.  I will talk about joint work with Joerg Brendle, Andre Nies and Selwyn Ng, where we flesh out this analogy for the cardinal characteristics of Cichon's diagram (amongst others), obtaining a diagram of highness properties which gives a context for many previously known results.  Particularly notable is that the analogy is not perfect, and whilst much of the diagram remains the same, some of it collapses.