Mathematical logic seminar – Oct 16 2012
Time: 12:00 – 13:20
Room: Wean Hall 7201
Speaker: Chris Lambie-Hanson
Department of Mathematical Sciences
Carnegie Mellon University
Title: Covering Matrices and Squares, Part I
Covering matrices were introduced by Matteo Viale in his proof that the Singular Cardinals Hypothesis follows from the Proper Forcing Axiom. In particular, he showed that PFA implies that certain covering matrices exhibit strong covering and reflection properties. In this series of talks, I will construct counterexamples to these covering and reflection properties and investigate their relationships with square principles. This will lead to an examination of a variety of square principles intermediate between $\square_\kappa$ and $\square(\kappa^+)$. In the first lecture, I will introduce the notion of a covering matrix and present results about the existence of certain types of $\kappa$-covering matrices for $\kappa^+$.