Series: Penn State Logic Seminar Date: Tuesday, March 2, 2004 Time: 2:30 - 3:45 PM Place: 307 Boucke Building Speaker: Elizabeth Brown, James Madison University, Mathematics Title: Some Minimality Problems Abstract: It is well known that forcing with partial orders whose conditions are trees or tree-like objects defined on omega generates a minimal degree of constructibility. We will discuss the generation of minimal degrees of constructibility via trees defined over uncountable cardinals, and the problem of consistent initial segments of the constructible degrees.