2006-01-26Martin Goldstern (TU Wien)Shelah's preservation theorems in RCS iterations
2006-03-02Sy Friedman (KGRC)The Inner Model Hypothesis
2006-03-09Sebastiaan Terwijn (TU Wien)Randomness and relativization
This will be an informal low-brow talk on some recent developments in recursion theory on random and generic sets. We will discuss several relations between randomness of finite strings and the theory of finite strings (Kolmogorov complexity). As it turns out, the notion of relativized computation plays a crucial role here. This is joint work with Andre Nies (Auckland) and Frank Stephan (Sydney).

2006-03-16Otmar Spinas (Kiel University)Perfect Set Theorems
2006-03-23John Krueger (KGRC)Internal Approachability and Reflection
2006-03-30Martin Goldstern (TU Wien)All creatures great and small
For any regular uncountable cardinal lambda I will describe a "creature-based" lambda^+-complete forcing notion that introduces a "wild" ultrafilter on lambda.
Assuming 2^lambda=lambda^+, we can find a sufficiently generic filter on this forcing notion; this allows us to construct a clone on lambda which is not contained in any coatom of the clone lattice, solving an old problem in clone theory. (These notions will be explained in the talk.)

I have sketched a corresponding result for lambda=omega in my talk in November 2002. Both results are a joint work with Saharon Shelah.

I will give a related talk (that concentrates on the algebraic rather than set-theoretic background) in the algebra seminar at TU Wien on April 7, 2006. []

2006-04-06Sy D. Friedman (KGRC)Forcing Condensation
2006-05-04Meeri Kesälä (University of Helsinki)Finitary Abstract Elementary Classes
We know that first order logic fails to capture many natural classes of structures that appear in mathematics. Several generalizations of model-theoretical tools to non-elementary classes (Shelah 1985) is very general. We do not study structures in any specific language, but give axioms for an abstract elementary substructure-relation. However, if we want to study for example stability theory in this context, we may have to add some more specific assumptions for the class. We introduce finitary abstract elementary classes, a subclass of abstract elementary classes with many good properties. We also compare finitary classes to some other non-elementary classes by studying the behaviour of Galois types and category transfer. This is joint work with Tapani Hyttinen.

2006-05-11John Krueger (KGRC)Some Consistency Results Related to Approachability
2006-06-01James Cummings (Carnegie Mellon University)Rainbow Ramsey Theory
2006-06-08James Cummings (Carnegie Mellon University)Rainbow Ramsey Theory Continued
2006-06-22Sy D. Friedman (KGRC)Square on the singular cardinals
2006-10-12Sy D. Friedman (KGRC)Measure-one covering relative to HOD
2006-10-19Katie Thompson (KGRC)Global complexity and internal consistency
2006-11-09Richard Kaye (University of Birmingham)Nonstandard symmetric groups
A nonstandard symmetric group is an internal finite symmetric group Sn inside a nonstandard model M of PA. This group can be considered internally as well as externally. Internally, it has a normal subgroup An of index 2, and An is simple for n>=5.

However, externally, An is an infinite group with an interesting normal subgroup structure. The main part of this talk will explain these normal subgroups of An. We conclude by examining interesting topological structures that can be imposed on these groups.

This is joint work with John Allsup, Birmingham.

2006-11-16Natasha Dobrinen (KGRC)Internal consistency and co-stationarity of the ground model
2006-11-23Pavel Ondrejovic (KGRC)Internal consistency and Easton's Theorem
2006-11-30Heike Mildenberger (KGRC)The Filter Dichotomy Principle and the Near Coherence of Filters Principle
2006-12-07Andrew Brooke-Taylor (KGRC)Large cardinals and definable well-orders
I will show how, using Kurepa trees as oracles, one may perform a class forcing so that a generically chosen class of cardinals will be definable in the extension. In the extension model, we will then have a definable well order, GCH will hold, and any n-superstrong cardinals from the ground model will remain n-superstrong.

For further, light-hearted discussion, see []

2006-12-14Jakob Kellner (KGRC, The Hebrew University of Jerusalem)Precipitous ideals and related games