Past Seminars- Logic Set Theory

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  • Logic Set Theory
    The structure of ideals II
    Monroe Eskew
    Mon Mar 12, 2012
    4:00 pm
    We present a proof of a theorem of Gitik and Shelah that places limits on the structure of quotient algebras by sigma-additive ideals. We will start by showing connections between Cohen forcing and Baire category on the reals. Then by using generic ultrapowers, we will prove that no sigma-additive ideal yields an atomless algebra with a countable...
  • Logic Set Theory
    The Structure of Ideals
    Monroe Eskew
    Mon Mar 5, 2012
    4:00 pm
    We present a proof of a theorem of Gitik and Shelah that places limits on the structure of quotient algebras by sigma-additive ideals. We will start by showing connections between Cohen forcing and Baire category on the reals. Then by using generic ultrapowers, we will prove that no sigma-additive ideal yields an atomless algebra with a countable...
  • Logic Set Theory
    The Urysohn sphere is rosy
    Dr Isaac Goldbring
    Mon Feb 27, 2012
    4:00 pm
    I will discuss the role that independence relations play in modern model theory, discussing the classes of stable, simple, and rosy theories along the way. I will then discuss why the Urysohn space is not stable or simple, but is rosy. Part of the talk reflects joint work with Clifton Ealy.
  • Logic Set Theory
    The ineffable tree property II
    Spencer Unger
    Wed Feb 15, 2012
    4:00 pm
    In this series of two talks I will give an introduction to some of my recent research on the ineffable tree property. The ineffable tree property is a two cardinal combinatorial principle which can consistently hold at small cardinals. My recent work has been on generalizing results about the classical tree property to the setting of the...
  • Logic Set Theory
    The ineffable tree property I
    Spencer Unger
    Mon Feb 13, 2012
    4:00 pm
    In this series of two talks I will give an introduction to some of my recent research on the ineffable tree property. The ineffable tree property is a two cardinal combinatorial principle which can consistently hold at small cardinals. My recent work has been on generalizing results about the classical tree property to the setting of the...
  • Logic Set Theory
    Definability in Urysohn's metric space
    Dr Isaac Goldbring
    Mon Feb 6, 2012
    4:00 pm
    Continuous logic is a relatively new logic better equipped for studying the model theory of structures based on complete metric spaces. There are continuous analogs of virtually every notion and theorem from classical model theory, often with equalities replaced by approximations. However, most of the work done in continuous logic has centered...
  • Logic Set Theory
    Martin-Solovay tree II
    Andres Forero
    Mon Jan 30, 2012
    4:00 pm
    We complete the construction of the Martin-Solovay tree