
Geoff Galgon
Mon Nov 23, 2015
4:00 pm
We continue our discussion of perfect and scattered subsets in the generalized Cantor space. We give some properties of the \kappatopologies over 2^{\lambda} introduced earlier (for \kappa \leq \lamba), define a CantorBendixon process for forests, and begin work on showing the consistency of CantorBendixon theorem analogues for closed subsets...

Geoff Galgon
Mon Nov 16, 2015
4:00 pm
We continue our discussion of perfect and scattered subsets in the generalized Cantor space. We we continue our study of the collection of topologies over 2^{\lambda} introduced last time. These topologies rely on the notion of a P_{\kappa}\lambdaforest, which is a natural generalization of a tree.

Southern California Logic Group
Sat Nov 14, 2015
10:00 am
This is the Fall 2015 intercampus CaltechUCLAUCI meeting.

Geoff Galgon
Mon Nov 9, 2015
4:00 pm
We continue our discussion of perfect and scattered subsets in the generalized Cantor space. This week we finish the proof of the fact that \kappaclosed forcings don't add branches to \kappascattered subsets of 2^{\kappa}. We then introduce a collection of topologies over 2^{\lambda} whose restrictions to P_{\kappa}\lambda have some...

Geoff Galgon
Mon Nov 2, 2015
4:00 pm
We continue our discussion of perfect and scattered subsets in the generalized Cantor space. We focus this week on generalizing the games played on subsets of 2^{\omega} considered previously to the 2^{\kappa} context, and introduce alternate notions of \kappaperfect and \kappascattered. We show that \kappaclosed forcings can’t add...

Geoff Galgon
Mon Oct 26, 2015
4:00 pm
We continue our discussion of perfect and scattered subsets in the generalized Cantor space. We focus in particular this week on constructing certain types of trees in 2^{<\kappa} for uncountable \kappa which exhibit fundamentally different behavior than trees in 2^{<\omega} can, from the perspective of adding branches, cardinal dichotomies...

Geoff Galgon
Mon Oct 19, 2015
4:00 pm
We will initially discuss games played on subsets of the Cantor space, for which the existence or nonexistence of winning strategies for certain players can provide a characterization of perfectness or scatteredness. We will also give an old characterization of the type of trees in 2^{<\omega} through which outer models can add...