Spring 2012

Set Theory Seminar

Our seminars are on Wednesdays, 10:40 a.m. - 11:30 a.m. in ILC 301

January  25
Speaker: Marion Scheepers

Remainder strategies in meager-nowhere dense games
We continue the series of talks on the existence of remainder strategies started in the Fall. Two remaining items from that series were to give the proofs of theorems of Just and of Galvin about cases where player TWO does not have a winning remainder strategy.
Just's theorem is that if ONE chooses countable subsets of omega_1, and TWO chooses finite sets, and if ONE is required to obey the rule that ONE's next choice is equal to, or contains, ONE's previous choice, then TWO does not have a remainder strategy that ensures that after omega innings TWO covers all the points covered by ONE's sets.
Galvin's theorem is a strengthening of Just's in that it shows that even if we put further strong restrictions on what ONE is allowed to do, TWO still does not have a winning remainder strategy. 

February 1
Speaker:  Bruno A. Pansera, University of Messina, Italy

Cardinal Functions and Monotonically Weakly Lindelof Spaces
The monotone Lindelof property introduced by Matveev in 1994 is stronger than the classical Lindelof property, while the weakly Lindelof property introduced in 1959 by Frolik is weaker than the classical Lindelof property. In joint work with Bonanzinga and Cammaroto [pdf] we recently introduced the weakly monotonically Lindelof property. It is intermediate in strength between monotonically Lindelof and weakly Lindelof. In this talk we give some examples and counterexamples of monotonically weakly Lindelof spaces and we discuss some properties involving cardinal functions for such spaces.

February 8
Speaker:  Bruno A. Pansera, University of Messina, Italy