2005-01-13John Krueger (KGRC)Supercompact Radin Forcing
2005-01-18Martin Goldstern (TU Wien)Continuous Fraisse conjecture and the number of Gödel logics
Linear orders are naturally quasiordered by embeddability. Answering a question of Fraisse, Laver showed that this quasiorder, restricted to the scattered linear orders (those that do not contain a copy of the rationals), is a well-quasi-order; he also showed that there are exactly aleph1 equivalence classes (modulo bi-embeddability) of countable linear orders. In a joint paper with Arnold Beckmann and Norbert Preining we generalize this theorem to the natural quasiorder that is given by CONTINUOUS embeddability. A Gödel logic is given by a closed subset G of the unit intervall (containing 0 and 1). Fuzzy (relational) G-models are sets M with maps M^k -> G for every k-ary predicate symbol. A fuzzy satisfaction function is defined naturally; the "Gödel logic" associated with G is the set of all sentences which have value 1 in every fuzzy G-model. All these logics are contained in the set of classical validities; as an application of the continuous Fraisse conjecture, we show that there are only countably many Gödel logics.

2005-04-05Sy-David Friedman (KGRC)Forcing with finite conditions
2005-04-12David Schrittesser (KGRC)Sigma-1-3 Absoluteness for ccc forcing and lightface indescribable cardinals
2005-04-19Andrew Brooke-Taylor (MIT)Critical Points of Rank-to-Rank Embeddings
One of the strongest large cardinal axioms we have posits the existence of an elementary embedding j from V_\lambda to V_\lambda for some limit ordinal \lambda. A peculiarity of it is that one such j will generate infinitely many more, not only through composition but also through the process of applying oneembedding to the graph of another.
I will talk about the structure generated in this way, and in particular the critical points of these embeddings.

2005-04-26Sy Friedman (KGRC)The inner model hypothesis
2005-05-03Andres Caicedo (KGRC)Preserving sequences of stationary subsets of omega_1
Let M be an inner model that computes omega_1 correctly. We study whether we can find in M a partition of omega_1 into infinitely many sets that are stationary from the point of view of V.

2005-05-10Sy Friedman (KGRC)Inner models and 0#
2005-05-24John Krueger (KGRC)Namba forcing, Chang's Conjecture, and Games
2005-06-07Jakob Kellner (TU Wien)A construction for non wellfounded forcing iterations
I will show how to "countable-support-iterate" finitely splitting lim-sup tree forcings along arbitrary total orders. (Part of a joint work with S. Shelah called Saccharinity)

2005-06-14John Krueger (KGRC)Combinatorial Principles Related to Adding Clubs
A number of forcing posets have been defined which introduce a club subset to a given fat stationary subset of \(\omega_2\) under various assumptions. I introduce a combinatorial property of \(\omega_2\) which implies there exists a fat stationary subset of \(\omega_2\) which cannot acquire a club subset by any forcing poset which preserves \(\omega_1\) and \(\omega_2\), answering a problem of Abraham and Shelah. This property follows from Martin's Maximum and is equiconsistent with a Mahlo cardinal.

2005-06-21Jakob Kellner (TU Wien)A construction for non wellfounded forcing iterations, Part II
See [[Talks/2005/06-21]]
2005-06-28Andres Caicedo (KGRC)BPFA and the reals
This is joint work with Boban Velickovic. I present some recent results (building on techniques introduced by Justin Moore) that allow us to code reals by ordinals in the presence of BPFA. I will also present some applications.

2005-10-06Katie Thompson (KGRC)Methods for solving universality problems
We will discuss a number of ways of showing that universal models do or do not exist. The methods stem from model theory, set theory and category theory. We will see examples of these methods mostly using relational structures, but they can be applied to algebraic and topological structures as well. By comparing which methods work for different structures, one can find patterns in the behaviour of these structures with regard to universality.

2005-10-13Mirna Dzamonja (UEA, Norwich)Measures on Boolean algebras
2005-10-20Tomas Jech (Czech Academy, Prague)Weak distributivity and a problem of von Neumann
2005-11-03Agatha Walczak-Typke (KGRC)The model theoretic structure of Dedekind-finite sets
2005-11-10Heike Mildenberger (KGRC)Separating some cardinal characteristics by oracle c.c. forcing
2005-11-24John Krueger (KGRC)Strong Reflection Principles
2005-12-01Natasha Dobrinen (KGRC)Co-stationarity of the ground model
2005-12-15Andrew Brooke-Taylor (KGRC)Vopěnka's principle and Category Theory