Past Seminars- Logic Set Theory

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  • Logic Set Theory
    Basic notions of effective descriptive set theory II
    Geoff Galgon and Garrett Ervin
    Mon Oct 24, 2011
    4:00 pm
    We will introduce the "lightface" projective hierarchy and examine it both from syntactical and semantical aspect. "Lightface" \Sigma^0_1" sets are effective versions of open sets. We also prove that lightface \Sigma^0_1 sets of reals can be represented as sets of branches of recursive trees, and lithtface \Sigma^1_1 sets can be represented as...
  • Logic Set Theory
    Basic notions of effective descriptive set theory.
    Geoff Galgon and Garrett Ervin
    Mon Oct 17, 2011
    4:00 pm
    We will introduce the "lightface" projective hierarchy and examine it both from syntactical and semantical aspect. "Lightface" \Sigma^0_1" sets are effective versions of open sets. We also prove that lightface \Sigma^0_1 sets of reals can be represented as sets of branches of recursive trees, and lithtface \Sigma^1_1 sets can be represented as...
  • Logic Set Theory
    Compactness and tower forcing
    Dr Sean Cox
    Mon Oct 10, 2011
    4:00 pm
    There are several examples in the literature where compactness properties of a cardinal $\kappa$ imply "bad" behavior of certain generic ultrapowers with critical point $\kappa$; particularly generic ultrapowers associated with tower forcings (Woodin's stationary tower forcing is an example of a tower forcing). I will discuss instances of this...
  • Logic Set Theory
    The Diagonal Reflection Principle and well-determined ultrapowers II
    Dr Sean Cox
    Mon Oct 3, 2011
    4:00 pm
    I will discuss the Diagonal Reflection Principle (DRP), which is a highly simultaneous form of stationary set reflection that follows from strong forcing axioms like $PFA^{+\omega_1}$. DRP can be viewed as a weaker version of the statement "there is a normal ideal with completeness $\omega_2$ whose associated poset is proper (i.e. preserves...
  • Logic Set Theory
    The Diagonal Reflection Principle and well-determined generic ultrapowers
    Dr Sean Cox
    Mon Sep 26, 2011
    4:00 pm
    I will discuss the Diagonal Reflection Principle (DRP), which is a highly simultaneous form of stationary set reflection that follows from strong forcing axioms like $PFA^{+\omega_1}$. DRP can be viewed as a weaker version of the statement "there is a normal ideal with completeness $\omega_2$ whose associated poset is proper (i.e. preserves...
  • Logic Set Theory
    Generic Elementary Embeddings II
    Monroe Eskew
    Mon May 23, 2011
    4:00 pm
  • Logic Set Theory
    Recent uses of infinitary methods in finite combinatorics
    Professor James Cummings
    Mon May 16, 2011
    4:00 pm
    In recent years there have been striking applications of infinitary methods in finite combinatorics. I will survey some of these methods, notably the theory of "flag algebras" due to Razborov.