2012: Miniworkshop set theory

June 20-22 a miniworkshop on set theory is held at the KGRC, supported by Mobility grant CR/Austria MEB601106.

Here is the program:

Wednesday 20th

3.30pmCoffee break
4.00pmS.-D.FriedmanOn the consistency strength of PFA


A long-standing open question is whether Baumgartner's result Con(supercompact) implies Con(PFA) can be reversed. The traditional approach to this problem is core model theory, which at present cannot yield consistency strengths past Woodin cardinals. In joint work with Peter Holy, based on some earlier work of Neeman, I'll show that it is consistent that there is a proper class of subcompact cardinals with PFA failing in all proper forcing extensions of the universe. This "quasi lower bound" provides some evidence that the consistency strength of PFA is beyond subcompactness. I'll also mention analogous work of Viale-Weig, which is based on entirely different methods.


Generalised Amoeba forcing and measurability


Amoeba for Silver which does not add Cohen reals, and we discuss some applications and open questions about Σ12-measurability.


Thursday 21st

9.00amCoffee break
9:30amV.DimonteRank-to-rank hypotheses and the failure of GCH
10:30amJ.FlaskovaSummable ideals and ultrafilters
11.10amCoffee break
11:30amY.KhomskiiAleph-1 Perfect MAD Families
2:00pmD.BartosovaUltrafilter dynamical system and its applications
3:00pmJ.StaryCoherent Structures on Boolean Algebras
3.40pmCoffee break

Internality in model theory and category theory


I will explain the model theoretic notion of internality, which provides conditions for the automorphism group of a structure over a reduct to be definable (in the original structure). I will then explain how the assumptions can be stated in a general categorical framework, and state a weak version of the main theorem, that holds in the categorical setting.

5:00pmD.ChodounskyGames for filters and towers

Friday 22nd

9.30amCoffee break
10.00amS.FuchinoReflection number of Rado Conjecture and Fodor-type reflection
11.00amM.DouchaBorel equivalence relations and Laver forcing