# Cichon's diagram for Turing oracles

**Date**: Wednesday 29 November 2017, 14:00 – 15:00**Location**: Mathematics Level 8, MALL 2, School of Mathematics**Type**: Proofs, constructions and computations seminars, Pure Mathematics seminars, Seminar series**Cost**: Free

#### 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.