MiniSymposium Speakers
Invited Speakers 
Contributing Speakers 


Schedule
Monday 3rd September, 2018
Talks are 25 minutes long with 5 minutes for questions.
14:00  Salma Kuhlmann 
14:30  Diana Carolina Montoya 
15:00  Kaisa Kangas 
15:30  Šárka Stejskalová 
16:00  Charlotte Kestner 
16:30  Heike Mildenberger 
Talk Titles and Abstracts
Salma Kuhlmann  University of Konstanz, Germany
Title: From Gödel's Incompleteness Theorem to Real Algebra
Abstract: Gödel's celebrated Theorem (which established among others the incompleteness of Peano arithmetic) has triggered great interest in the study of fragments of arithmetic in general, and in particular in finding explicit constructions of their models. In this talk, I will explain the interrelation between models of arithmetic on the one hand, and integer parts of real closed fields on the other. I will thereby highlight the interplay between the first order deductive closure of these theories versus the algebraic properties of these commutative domains.
Diana Carolina Montoya  Kurt Gödel Research Center, Vienna, Austria
Title: Infinite combinatorics on the generalized Baire spaces
Abstract: The study of various classic set theory concepts on the generalized Baire spaces has been a subject of special interest on the last years. One specific example corresponds to the generalization of some classical cardinal invariants to this context. I will present a survey of some of the classical results and their counterparts in the extended case.
Kaisa Kangas  University of Helsinki, Finland
Title: Categoricity and Universal Classes
Abstract: One example of a universal class is the class of models of a model complete first order theory. More generally, an abstract elementary class $(\mathcal{K}, \preccurlyeq)$ is universal if $\preccurlyeq$ is the submodel relation $\subseteq$ and for all models $\mathcal{A} \subseteq \mathcal{B} \in \mathcal{K}$, we have $\mathcal{B} \in \mathcal{K}$. In our work on universal classes, the aim was to find out whether a version of the the following statement is true: "Suppose $\mathcal{K}$ is a universal class with $LS(\mathcal{K})=\lambda$ and $\mathcal{K}$ is categorical in some cardinal $\kappa > \lambda$. Then $\mathcal{K}$ is categorical in every $\xi>\lambda$ and the models of $\mathcal{K}$ are either vector spaces or trivial (in the sense that the geometry is disintegrated)." The interesting part of the statement is that the models would be either vector spaces or trivial, which means that the reason behind the categoricity would be in the realm of classical mathematics. We proved that the statement holds after removing some "noise" from the class. In this talk, I will briefly discuss the background, present our result and discuss its implications.
Šárka Stejskalová Kurt Gödel Research Center, Vienna, Austria
Title: The tree property
Abstract: We will discuss the tree property and its effect on the continuum function. For a regular cardinal $\kappa$, we say that $\kappa$ has the tree property if there are no $\kappa$Aronszajn trees. It is known that the tree property has the following nontrivial effect on the continuum function:
(*) If the tree property holds at $\kappa^{++}$, then $2^{\kappa} > \kappa^{+}$.
We will present original results regarding the tree property which suggest that (*) is the only restriction which the tree property puts on the continuum function in addition to the usual restrictions provable in ZFC.
Charlotte Kestner  Imperial College, London, UK
Title: Some results in distal theories Nonforking formulas in distal NIP theories
Slides from Charlotte Kestner's talk.
Abstract: One of the aims of model theory is to classify mathematical structures according to properties of their definable sets. I will give an introduction to distal theories, a relatively new area of the classification that has received a lot of attention recently. I will then go on to discuss some results in distal theories. In particular, time allowing, I will discuss the definable $(p,q)$theorem for distal theories, and the more recent result that $T$ is distal provided it has a model $\mathcal{M}$ such that the theory of the Shelah expansion of $\mathcal{M}$ is distal. This is joint work with G. Boxall.
Heike Mildenberger  AlbertLudwigs University of Freiburg, Germany
Title: Preserving a $P$Point and Diagonalising an Ultrafilter
Abstract: We show that under CH there is a forcing that preserves a $P$point and diagonalises another ultrafilter. We report on our work towards iterating such a procedure.