**April 22**

Andreas Blass,
University of Michigan

**Do these ultrafilters exist, I: preservation by forcing**

This is the first of two talks devoted to two properties of ultrafilters (non-principal, on omega) for which the question 'Do such ultrafilters exist?' is open. In this talk, I'll discuss the property of being preserved by some forcing that adds new reals. Some forcings destroy all ultrafilters, and some (in fact many) ultrafilters are destroyed whenever new reals are added, but it is consistent with ZFC that some ultrafilters are preserved when some kinds of reals are added. I plan to prove some of these things and describe the rest. I'll also describe a combinatorial characterization, due to Arnie Miller, of preservable ultrafilters.