Past Seminars- Logic Set Theory

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  • 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 \kappa-topologies over 2^{\lambda} introduced earlier (for \kappa \leq \lamba), define a Cantor-Bendixon process for forests, and begin work on showing the consistency of Cantor-Bendixon 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}\lambda-forest, 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 Caltech-UCLA-UCI 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 \kappa-closed forcings don't add branches to \kappa-scattered 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 \kappa-perfect and \kappa-scattered. We show that \kappa-closed 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...