## Yann Pequignot: Sigma^1_2 sets and countable Borel chromatic numbers

Friday, July 21th, 2017, 10.00-12.00

Aula S, Palazzo Campana, Università di Torino

Speaker: Yann Pequignot (University of California, Los Angeles)

Title: Sigma^1_2 sets and countable Borel chromatic numbers

Abstract:

Analytic sets enjoy a classical representation theorem based on wellfounded relations. I will explain a similar representation theorem for Sigma^1_2 sets due to Marcone. This can be used to answer negatively the primary outstanding question from (Kechris, Solecki and Todorcevic; 1999): the shift graph is not minimal among the graphs of Borel functions which have infinite Borel chromatic number.

## Dima Sinapova: Iterating Prikry Forcing

Monday, June 26th, 2017, 10.30-12.00

Aula Lagrange, Palazzo Campana, Università di Torino

Speaker: Dima Sinapova (University of Illinois at Chicago)

Title: Iterating Prikry Forcing

Abstract:

We will present an abstract approach of iterating Prikry type forcing. Then we will use it to show that it is consistent to have finite simultaneous stationary reflection at $\kappa^+$ with not SCH at $\kappa$. This extends a result of Assaf Sharon. Finally we will discuss how we can bring the construction down to $\aleph_{\omega}$. This is joint work with Assaf Rinot.