# 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

SpeakerTitleAbstract/Slides
Juan AguileraThe botanics of provability (and $\omega^\omega$ other short stories). slides
Szymon ŻeberskiAn example of a capacity for which all positive Borel sets are thick slides
Tomasz ŻuchowskiNonseparable growth of $\omega$ supporting a strictly positive measureabstract slides
Taras BanakhThe Steinhaus properties of $\sigma$-ideals on Polish groups slides
Hector Alonso Barriga AcostaOn discretely generated box productsabstract slides
Adam BartošOn maximal connected topologiesabstract slides
Jeffrey BergfalkStrong Homology and Set Theory slides
Mariam BeriashviliOne Concrete Application of Point Set Theory in Measure Theoryabstract slides
Filippo CalderoniOn the complexity of embeddability between groupsabstract slides
Jonathan Cancino-ManríquezTrees on $\mathcal{P}(\omega)/\mathrm{fin}$abstract slides
Aleksander CieślakFilters and sets of Vitali type slides
Sakae FuchinoReflection numbers under large continuumabstract slides
Osvaldo GuzmanThe principle (*) of Sierpinski and a question of Millerabstract slides
Jialiang HeComparison game on trace idealsabstract slides
Jacob HiltonTopological Ramsey theory of countable ordinalsabstract slides
Radek HonzikThe tree property at the double successor of a singular with larger gapabstract slides
Joanna Jureczko$\kappa$-strong sequences and the existence of generalized independent families slides
Vladimir KanoveiSome applications of finite-support products of Jensen’s minimal $\Delta_3^1$ forcingabstract slides
Maria KidawaCube-like comlpexes and Poincare-Miranda Theoremabstract slides
Gonzalo Martínez CervantesOn weakly Radon-Nikodym compact spacesabstract slides
Arturo Antonio Martinez Celis RodriguezCombinatorics related to the Michael Space problemabstract slides
Diego Alejandro Mejía-GuzmanExpected values for the a.d. number and 3D-iterationsabstract slides
Marcin Michalski(Non)measurability of I-Luzin setsabstract slides
Diana Carolina Montoya The ultrafilter number for uncountable $\kappa$.abstract slides
Nenad MoracaReversibility of relational structuresabstract slides
Magdalena NowakCompact sets in Euclidean spaces as IFS-attractorsabstract slides
Mikhail PatrakeevLuzin $\pi$-bases and the foliage hybrid operationabstract slides
Aleksandar PavlovićLocal function vs. local closure functionabstract slides
José de Jesús Pelayo GómezA tall ideal in which player II has a winning strategy in the cut and choose gameabstract slides
Alejandro PovedaRosenthal compacta that are premetric of finite degreeabstract slides
Robert RałowskiUnions of regular families slides
Damian SobotaRosenthal families and the Grothendieck propertyabstract slides
Silvia SteilaSystems of Filtersabstract slides
Jarosław SwaczynaSome structural properties of ideal invariant injectionsabstract slides
Piotr SzewczakProducts of Menger spacesabstract slides
Przemysław TkaczThe Bolzano property.abstract slides
Andrea Vaccaro$C^*$-algebras and $\mathsf{B}$-names for Complex Numbersabstract slides
Wolfgang WohofskyNo large sets which can be translated away from every Marczewski null setabstract slides