Logic Seminar

I will show that Dilworth's theorem remains true in the Borel context: for a given natural number n, a Borel quasi-order ≤ on a Polish space X either contains an (n+1)-sized antichain, or X can be covered by n Borel chains. I will also discuss a generalization of a related theorem of Harrington, Marker, and Shelah, characterizing the existence of a perfect antichain.