# 2011 seminar talk: Cardinal Characteristics, Projective Wellorders and Large Continuum

Talk held by Vera Fischer (KGRC) at the KGRC seminar on 2011-10-13.

### Abstract

We present a method for controlling cardinal characteristics in the presence of a projective wellorder and $$2^\aleph_0>\aleph_2$$. This also answers a question of Harrington by showing that the existence of a (lightface) $$\Delta^1_3$$ wellorder of the reals is consistent with Martin's axiom and $$2^\aleph_0=\aleph_3$$. This is joint work with Sy-David Friedman and Lyubomyr Zdomskyy.