| date | speaker | title |
|---|---|---|
| 2006-01-26 | Martin Goldstern (TU Wien) | Shelah's preservation theorems in RCS iterations |
| 2006-03-02 | Sy Friedman (KGRC) | The Inner Model Hypothesis |
| 2006-03-09 | Sebastiaan 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). | ||
| 2006-03-16 | Otmar Spinas (Kiel University) | Perfect Set Theorems |
| 2006-03-23 | John Krueger (KGRC) | Internal Approachability and Reflection |
| 2006-03-30 | Martin 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. [http://www.dmg.tuwien.ac.at/fg1/seminar/20060407.html] | ||
| 2006-04-06 | Sy D. Friedman (KGRC) | Forcing Condensation |
| 2006-05-04 | Meeri 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. | ||
| 2006-05-11 | John Krueger (KGRC) | Some Consistency Results Related to Approachability |
| 2006-06-01 | James Cummings (Carnegie Mellon University) | Rainbow Ramsey Theory |
| 2006-06-08 | James Cummings (Carnegie Mellon University) | Rainbow Ramsey Theory Continued |
| 2006-06-22 | Sy D. Friedman (KGRC) | Square on the singular cardinals |
| 2006-10-12 | Sy D. Friedman (KGRC) | Measure-one covering relative to HOD |
| 2006-10-19 | Katie Thompson (KGRC) | Global complexity and internal consistency |
| 2006-11-09 | Richard 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. | ||
| 2006-11-16 | Natasha Dobrinen (KGRC) | Internal consistency and co-stationarity of the ground model |
| 2006-11-23 | Pavel Ondrejovic (KGRC) | Internal consistency and Easton's Theorem |
| 2006-11-30 | Heike Mildenberger (KGRC) | The Filter Dichotomy Principle and the Near Coherence of Filters Principle |
| 2006-12-07 | Andrew 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 [http://www.logic.univie.ac.at/~andrewbt/DinosaurDWO.html] | ||
| 2006-12-14 | Jakob Kellner (KGRC, The Hebrew University of Jerusalem) | Precipitous ideals and related games |
