Logic Seminar
Dima Sinapova
UIC
The Tree property at successive cardinals
Abstract: The tree property is a reflection type combinatorial principle.
It holds at $\omega$ (Konig's infinity lemma),
fails at $\omega_1$ (Aronszajn) and can consistently hold at
$\omega_2$ (Mitchell).
More generally, it is a remnant of large cardinals,
but can hold at successor cardinals. A long standing project in set theory
is to try to obtain the tree property at every regular cardinal
greater than $\omega_1$.
We will start by introducing some classical results.
Then I will discuss a recent result that assuming large cardinals,
one can consistently get the tree property at the first and second
successor of a singular strong limit cardinal.
Tuesday September 29, 2015 at 4:00 PM in SEO 427