Time:  12:00  13:20 
Room: 
Wean Hall 7201

Speaker: 
Chris LambieHanson Department of Mathematical Sciences Carnegie Mellon University 
Title:  Covering Matrices and Squares, Part II

Abstract: 
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. In the first lecture, we showed that the existence of transitive, normal, uniform covering kappacovering matrices for kappa^+ follows from square_{kappa, < kappa} (but not from weak square). In the second lecture, we will show that the converse fails by constructing a model in which there is a transitive, normal, uniform kappacovering matrix for kappa^+ but in which square_{kappa, < kappa} fails. If time permits, we will begin a discussion of Todorcevic's rhofunctions on square sequences and their use in constructing covering matrices. 