Past Seminars- Logic Set Theory

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  • Logic Set Theory
    Foreman's Duality Theorem and Applications II
    Monroe Eskew
    Mon May 13, 2013
    4:00 pm
  • Logic Set Theory
    Foreman's Duality Theorem and Applications I
    Monroe Eskew
    Mon May 6, 2013
    4:00 pm
    We present a theorem of Foreman that allows an exact characterization of what happens to the structure of precipitous ideals after suitable forcing. This theorem unifies several well-known results, giving as them quick corollaries. We will use it to show: forcing precipitous ideals from large cardinals, preservation theorems of Kakuda and...
  • Logic Set Theory
    Dense ideals from determinacy II
    Trevor Wilson
    Mon Apr 29, 2013
    4:00 pm
    Under the Axiom of Determinacy, the least uncountable cardinal omega_1 behaves like a large cardinal. We will present a theorem due to Woodin saying that from a strong form of determinacy, namely AD_R + "Theta is regular," one can force the Axiom of Choice together with the statement "there is an omega_1-dense ideal on omega_1....
  • Logic Set Theory
    Dense ideals from determinacy I
    Trevor Wilson
    Mon Apr 22, 2013
    4:00 pm
    Under the Axiom of Determinacy, the least uncountable cardinal omega_1 behaves like a large cardinal. We will present a theorem due to Woodin saying that from a strong form of determinacy, namely AD_R + "Theta is regular," one can force the Axiom of Choice together with the statement "there is an omega_1-dense ideal on omega_1....
  • Logic Set Theory
    ISP, guessing models, and PFA III
    Christoph Weiss
    Mon Apr 15, 2013
    4:00 pm
    We complete our introduction to the principle ISP and its relatives as well as their connections to supercompact cardinals and the proper forcing axiom. As a consequence of our analysis we give a proof that all known forcing constructions of models satisfying PFA require very large cardinals.
  • Logic Set Theory
    ISP, guessing models, and PFA II
    Christoph Weiss
    Mon Apr 8, 2013
    4:00 pm
    We continue with an introduction to the principle ISP and its relatives as well as their connections to supercompact cardinals and the proper forcing axiom. In particular, we prove that PFA implies ISP.
  • Logic Set Theory
    ISP, guessing models, and PFA
    Christoph Weiss
    Mon Apr 1, 2013
    4:00 pm
    We give an introduction to the principle ISP and its relatives as well as their connections to supercompact cardinals and the proper forcing axiom.