Past Seminars- Logic Set Theory

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  • Logic Set Theory
    Silver's model for failure of SCH
    Ryan Holben
    Mon Oct 15, 2012
    4:00 pm
    The classical result of Silver -- construction of the model where the Singular Cardinal Hypothesis fails -- will be presented. The emphasis is on presenting Easton suport iteration and extension of elementary embedding to a generic extension of the universe, which is the key ingredient of the entire construction.
  • Logic Set Theory
    Coding reals by clubs in $[\omega_2]^\omega$
    Sean Cox
    Mon Oct 8, 2012
    4:00 pm
    In the 80s Gitik proved the following theorem: For every real $x$ and every club $D \subseteq [\omega_2]^\omega$, there are $a,b,c \in D$ such that $x \in L(a,b,c)$. An immediate corollary of Gitik's theorem is: if $W$ is a transitive $ZF^-$ model of height at least $\omega_2$ such that $W$ is missing some real, then the complement of $W$ is...
  • Logic Set Theory
    Natural strengthenings of the tree property -- an introduction to ITP and ISP II
    Christoph Weiss
    Mon Jun 11, 2012
    4:00 pm
    We will present the combinatorial principles ITP and ISP, discuss how they strengthen the tree property, and talk about their relative consistency
  • Logic Set Theory
    Natural Strengthenings of the Tree Property -- An Introduction to ITP and ISP
    Christoph Weiss
    Mon Jun 4, 2012
    4:00 pm
    We will present the combinatorial principles ITP and ISP, discuss how they strengthen the tree property, and talk about their relative consistency.
  • Logic Set Theory
    A hierarchy of supercompactness measures in ZF+DC
    Nam Trang
    Thu May 24, 2012
    4:00 pm
    For each \alpha < \omega_1, let X_\alpha = \{f : \omega^\alpha \rightarro\powerset_{\omega_1}(\mathbb{R})| f is increasing and continuous} and \mu_\alpha be a normal fine measure on X_\alpha. We identify X_0 with \powerset_{\omega_1}(R). Martin and Woodin independently showed that these measures exist assuming (ZF + DC_\mathbb{R}) + AD +...
  • Logic Set Theory
    A bad scale and the failure of SCH at $\aleph_\omega$ III
    Dima Sinapova
    Mon May 21, 2012
    4:00 pm
    Starting from a supercompact, we construct a model in which SCH fails at $\aleph_\omega$ and there is a bad scale at $\aleph_\omega$. The existence of a bad scale implies the failure of weak square. The construction uses two Prikry type forcings defined in different ground models and a suitably defined projection between them. This is joint work...
  • Logic Set Theory
    Iterated forcing at successors of singular cardinals II
    James Cummings
    Tue May 15, 2012
    4:00 pm
    It is hard to find analogues of MA in which aleph_1 is replaced by the successor of a singular cardinal because a) The consequences of MA-like axioms have large consistency strength b) There is no satisfactory analogue of finite support ccc iteration Dzamonja and Shelah found an ingenious approach to proving results of this general kind. I will...