November 8
Iian Smythe,
Rutgers University
Parametrized diamonds and mad families of subspaces
In their 2004 paper, Moore, Hrusak and Dzamonja isolated a weakening of Jensen's diamond principle that could be 'parametrized' by a cardinal invariant, implies that the corresponding invariant is small, and yet is consistent with the failure of the Continuum Hypothesis. Moreover, these principles fully determine many cardinal invariants in 'canonical' models, those obtained by iterations of definable proper forcings. I will give a survey of this subject, and then describe a recent application in the study of maximal almost disjoint families of subspaces of a countably infinite-dimensional vector space.