## Past Seminars- Logic Set Theory

• 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...
• 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...
• 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...
• 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...
• 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...
• Monroe Eskew
Mon May 23, 2011
4:00 pm
• 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.