2003-01-09Rene Schipperus (KGRC)Differential games on Cardinal numbers
2003-01-16James Hirschorn (KGRC)Nonhomogeneous analytic families of trees, Part 1
2003-01-23James Hirschorn (KGRC)Nonhomogeneous analytic families of trees, Part 2
2003-01-30David Aspero (KGRC)Some results about bounded forcing axioms
2003-02-07Peter Koepke (Universität Bonn)On the Strength of Mutual Stationarity at Small Cardinals
2003-03-11David Aspero (KGRC)The nonexistence of nice forcings in inner models
2003-03-18Sy Friedman (KGRC)Forcing with finite conditions
2003-03-25Sy Friedman (KGRC)Forcing with finite conditions
2003-04-01Jakob Kellner (KGRC)Preserving non-null with transitive nep forcings
I will introduce the definitions of Suslin ccc, Suslin proper and transitive nep, demonstrate that many of the usual "definable" forcings of sets of reals are Suslin+, and present an application of these notions, a simplified version of Shelah's "preserving a little implies preserving much": If I is an ideal generated by a Suslin ccc forcing (e.g. null or meager), and P is a transitive nep forcing, and (in V and every forcing extension) P forces that no old positive Borel-set becomes null, then P forces that no old positive set becomes null.

2003-04-29Heike Mildenberger (KGRC)Needed reals for the cofinality relation on the Lebesgue nullsets
2003-05-06Ralf Schindler (KGRC)BMM is stronger than BSPFA
2003-05-20Martin Goldstern (TU Wien)A rigid structure with many (almost) automorphisms
2003-05-27Andrzej Roslanowski (University of Nebraska at Omaha)Around Sheva-Sheva-Sheva: forcing for the lambda-reals (where lambda is inaccessible)
A number of cardinal characteristics related to the Baire space, the Cantor space and/or the combinatorial structure of [omega]^omega can be extended to the spaces obtained by replacing omega by lambda (for any infinite cardinal lambda). Following the tradition of Set Theory of the Reals we may call cardinal numbers defined this way "cardinal characteristics of lambda-reals". The menagerie of those characteristics seems to be much larger than the one for the continuum, but to decide if the various definitions lead to different (and interesting) cardinals we need a well developed forcing technology. We will present initial steps in this direction. This is a joint work with Saharon Shelah.
2003-10-07Andres Caicedo (KGRC)Well-Orderings of the Reals and Real-valued Measurability
I will prove that (if there are measurables, then) there are extensions of V where the continuum is real-valued measurable and there is a Sigma-2-2 well-ordering of the reals. I will also show that natural strengthenings of the concept of real-valued measurability imply that the reals are not Sigma-2-n well-orderable for any n (so the result is not vacuously true) and that real-valued measurability implies that no well-ordering of the reals belongs to L(R) (so the result is non-trivial.) Depending on time, I might mention what is known with respect to real-valued measurability of the continuum and Sigma-2-1 well-orderings, which is a much more complicated story.

2003-10-14Andres Caicedo (KGRC)Well-Orderings of the Reals and Real-valued Measurability 2
2003-10-21Sy Friedman (KGRC)Set-Generic L-Saturation
2003-11-04Sy Friedman (KGRC)Generic Saturation and Absoluteness
2003-11-11Martin Goldstern (TU Wien)Continuous Ramsey Theory
2003-11-18Sy Friedman (KGRC)The Mutual Diamond Principle
2003-11-25Jakob Kellner (TU Wien)Preserving Preservation
We investigate sufficient conditions that allow to preserve (in limit setps of countable support interations) the property of preservation of positivity.

2003-12-02Jakob Kellner (TU Wien)Preserving Preservation 2
We investigate under which conditions preservation of positivity is iterable (joint work with S. Shelah).

2003-12-09Sy Friedman (KGRC)Definability Degrees