
Damir Dzhafarov
Mon Oct 3, 2016
4:00 pm
I will discuss recent investigations of various reducibility notions between Pi^1_2 principles of secondorder arithmetic, the most familiar of which is implication over the subsystem RCA_0. In many cases, such an implication is actually due to a considerably stronger reduction holding, such as a uniform (a.k.a. Weihrauch) reduction. (Here, we say...

Maxwell Levine
Mon Sep 26, 2016
4:00 pm
Abstract: The combinatorial properties of large cardinals tend to clash with those satisfied by G\"odel's constructible universe, especially the square property (denoted $\square_\kappa$) isolated by Jensen in the seventies. Strong cardinal axioms refute the existence of square, but it is possible with some finetuning to produce models...

Omer Ben Neria
Mon May 23, 2016
4:00 pm
The pursuit of better understanding the universe of set theory V motivated an extensive study of definable inner models M whose goal is to serve as good approximations to V. A common property of these inner models is that they are contained in HOD, the universe of hereditarily ordinal definable sets. Motivated by the question of how ``close"...

Grigor Sargsyan
Mon May 16, 2016
4:00 pm
We will compute the mantle, the intersection of all grounds, of the minimal class size mouse with a Woodin cardinal and a Strong cardinal.

Garrett Ervin
Mon May 9, 2016
4:00 pm
We complete the proof of the main theorem by showing that if X^3 is isomorphic to X, then X^{\omega} has a parityreversing automorphism. By our previous results this implies X^2 is isomorphic to X as well. The proof generalizes to show that for any n > 1, if X^n is isomorphic to X, then X^2 is isomorphic to X. Time permitting we will discuss...

Dima Sinapova
Mon May 2, 2016
4:00 pm
A remarkable theorem of Shelah states that if $\kappa$ is a singular strong limit cardinal of uncountable cofinality, then there is a subset $x$ of $\kappa$, such that $HOD_x$ contains the powerset of $\kappa$. We show that in general this is not the case for countable cofinality. Using a version of diagonal supercompact extender Prikry...

Garrett Ervin
Mon Apr 25, 2016
4:00 pm
We complete the proof of the main theorem by showing that if X^3 is isomorphic to X, then X^{\omega} has a parityreversing automorphism. By our previous results this implies X^2 is isomorphic to X as well. The proof generalizes to show that for any n > 1, if X^n is isomorphic to X, then X^2 is isomorphic to X. Time permitting we will discuss...