William Chen : Variations of the stick principle

Posted by Dima Sinapova , part of the Logic Seminar.

At

Sept. 26, 2017, 4 p.m.

In

SEO 427

Abstract

The stick principle is a weakening of Jensen's diamond that asserts that there is a family of infinite subsets of $omega_1$ so that any uncountable subset of $\omega_1$ has some member of the family as a subset. We will give a forcing construction to separate versions of the stick principle which put a bound on the order-type of the subsets in the family. Many open problems remain about the relationship between different variations of this principle, such as the existence of certain club-guessing sequences or Suslin trees, and we will describe some progress in this direction.