Tutorial Track
M. Goldstern: Iterated forcing
I will present some old and well-known facts about iterated forcing, and also give a few more recent constructions. In the first hour I will define iterated forcing and present the proof of "preservation of properness for countable support iterations", and if time permits, also sketch a preservation theorem. In the second lecture I will talk about some techniques that are useful for dealing with products (continuous reading, bigness and halving of creatures), and in the third lecture I will talk about finite support iterations.
T. Jech: Measure Algebras
In the 1930s, John von Neumann asked if measure algebras can be characterized algebraically, in particular, as Boolean $\sigma$-algebras that satisfy the countable chain condition and the weak distributivity law.
75 years – and extensive work by many mathematicians – later, we now know that the von Neumann conditions are not sufficient. However, in order to carry a sigma-additive measure it is sufficient (and necessary) that the algebra is weakly distributive and has the additional property that we call “uniformly concentrated”: there exists a choice function $F$ on finite antichains such that whenever $A_n$ is a sequence of antichains with $|A_n|\ge 2^n$ then the sequence ${F(A_n)}$ converges to $0$.
In the tutorial we give a complete self-contained proof of this result (for the lack of time we will use but not prove two classical mathematical results: the Hahn–Banach Theorem and Hall’s “Marriage” Theorem). No specialized knowledge is necessary; familiarity with convergence of sequences in a Boolean sigma-algebra would be helpful.
Y. Moschovakis: Effective descriptive set theory, what it is about
The subject is a common generalization of classical Descriptive Set Theory and Recursion Theory and my aim in this tutorial is to give an elementary exposition of a few of its fundamental ideas, notions and techniques. I will assume only some basic facts about recursive functions on the natural numbers, set theory and (metric) topology, what would normally be covered in a semester of an introductory class in each of these topics.
L. Zdomskyy: Menger spaces everywhere
The first lecture will be devoted to general properties of Menger and Hurewicz spaces. During the second one we'll discuss filters with these properties and the Mathias forcing associated to them. This lecture will be based on the article arxiv.org/pdf/1401.2283.pdf">Mathias Forcing and Combinatorial Covering Properties of Filters. The third lecture will be about topological Ramsey theory and be based on arxiv.org/pdf/1407.7437.pdf">Algebra, Selections and Additive Ramsey Theory.
Research Track
| Speaker | Title | Abstract/Slides |
|---|
| Juan Aguilera | The botanics of provability (and $\omega^\omega$ other short stories). | slides |
| Szymon Żeberski | An example of a capacity for which all positive Borel sets are thick | slides |
| Tomasz Żuchowski | Nonseparable growth of $\omega$ supporting a strictly positive measure | abstract slides |
| Taras Banakh | The Steinhaus properties of $\sigma$-ideals on Polish groups | slides |
| Hector Alonso Barriga Acosta | On discretely generated box products | abstract slides |
| Adam Bartoš | On maximal connected topologies | abstract slides |
| Jeffrey Bergfalk | Strong Homology and Set Theory | slides |
| Mariam Beriashvili | One Concrete Application of Point Set Theory in Measure Theory | abstract slides |
| Filippo Calderoni | On the complexity of embeddability between groups | abstract slides |
| Jonathan Cancino-Manríquez | Trees on $\mathcal{P}(\omega)/\mathrm{fin}$ | abstract slides |
| Aleksander Cieślak | Filters and sets of Vitali type | slides |
| Sakae Fuchino | Reflection numbers under large continuum | abstract slides |
| Osvaldo Guzman | The principle (*) of Sierpinski and a question of Miller | abstract slides |
| Jialiang He | Comparison game on trace ideals | abstract slides |
| Jacob Hilton | Topological Ramsey theory of countable ordinals | abstract slides |
| Radek Honzik | The tree property at the double successor of a singular with larger gap | abstract slides |
| Joanna Jureczko | $\kappa$-strong sequences and the existence of generalized independent families | slides |
| Vladimir Kanovei | Some applications of finite-support products of Jensen’s minimal $\Delta_3^1$ forcing | abstract slides |
| Maria Kidawa | Cube-like comlpexes and Poincare-Miranda Theorem | abstract slides |
| Gonzalo Martínez Cervantes | On weakly Radon-Nikodym compact spaces | abstract slides |
| Arturo Antonio Martinez Celis Rodriguez | Combinatorics related to the Michael Space problem | abstract slides |
| Diego Alejandro Mejía-Guzman | Expected values for the a.d. number and 3D-iterations | abstract slides |
| Marcin Michalski | (Non)measurability of I-Luzin sets | abstract slides |
| Diana Carolina Montoya | The ultrafilter number for uncountable $\kappa$. | abstract slides |
| Nenad Moraca | Reversibility of relational structures | abstract slides |
| Magdalena Nowak | Compact sets in Euclidean spaces as IFS-attractors | abstract slides |
| Mikhail Patrakeev | Luzin $\pi$-bases and the foliage hybrid operation | abstract slides |
| Aleksandar Pavlović | Local function vs. local closure function | abstract slides |
| José de Jesús Pelayo Gómez | A tall ideal in which player II has a winning strategy in the cut and choose game | abstract slides |
| Alejandro Poveda | Rosenthal compacta that are premetric of finite degree | abstract slides |
| Robert Rałowski | Unions of regular families | slides |
| Damian Sobota | Rosenthal families and the Grothendieck property | abstract slides |
| Silvia Steila | Systems of Filters | abstract slides |
| Jarosław Swaczyna | Some structural properties of ideal invariant injections | abstract slides |
| Piotr Szewczak | Products of Menger spaces | abstract slides |
| Przemysław Tkacz | The Bolzano property. | abstract slides |
| Andrea Vaccaro | $C^*$-algebras and $\mathsf{B}$-names for Complex Numbers | abstract slides |
| Wolfgang Wohofsky | No large sets which can be translated away from every Marczewski null set | abstract slides |