Series: Penn State Logic Seminar Date: Monday, October 29, 2001 Time: 10:10 - 11:00 AM Place: 320 Willard Building Speaker: Mirna Dzamonja, Mathematics, University of East Anglia Title: Some Usual and Some Unusual Combinatorial Principles Abstract: We discuss two recent papers. The first is joint with Michael Hrusak and Justin Moore and concerns various generalisations of the weak diamond which allow us to calibrate exactly how much of diamond is necessary for certain well-known constructions classicaly derived from diamond, such as that of a Suslin tree. These constructions are mostly limited to omega_1. The other paper by the speaker considers some classical diamond-like principles, such as club, but in the context of cardinals above beth_omega. Using pcf theory it is proved that certain versions of this principle at such cardinals follow simply from the relevant instances of GCH.