Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 13 April 2016, 17:00 hrs

Room: S17#05-11, Department of Mathematics, NUS

Speaker: Xu Tianyi

Title: Strong projective absoluteness

URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html

Abstract:

Strong projective absoluteness is the statement that

V[G_1]_{omega+1} < V[G_2]_{omega+1}. This can be expressed as

a statement about projective sets “retaining their identities”

across generic extensions. A universally Baire set is a set of reals

with a Suslin representation that can be computed in generic

extensions. We will show, under suitable large cardinal hypotheses,

that every projective set is universally Baire, and the construction

is canonical from the defining formula. From these strong projective

absoluteness can be deduced.

We will introduce the notion of (weakly) homogeneous trees, which

plays a crucial role in the construction. The large cardinals are

used to prove the (weak) homogeneity of certain trees.

This talk is based on Hugh Woodin’s 2014 talk in

the IMS Summer School in Logic.