# Tutorial Track

## L. Aurichi: Some games and their topological consequences

Alice and Bob are always playing games. Sometimes Alice plays points and Bob answers with open neighborhoods of the points (Alice wants to force Bob to cover the whole space). Some other times Alice and Bob play things related to density or tightness. Some games are short ($\omega$ innings), some others are longer ($\omega_1$ innings).

We will present some games and discuss the consequences of existence of winning strategies for some of the players.

slides I, slides II, slides III

## J. D. Hamkins: Set-theoretic potentialism

I shall introduce and develop the theory of set-theoretic potentialism. A potentialist system is a collection of first-order structures, all in the same language $\mathcal{L}$, equipped with an accessibility relation refining the inclusion relation. Any such system, viewed as an inflationary-domain Kripke model, provides a natural interpretation for the modal extension of the underlying language $\mathcal{L}$ to include the modal operators. We seek to understand a given potentialist system by analyzing which modal assertions are valid in it.

Set theory exhibits an enormous variety of natural potentialist systems. For example, with forcing potentialism, one considers the models of set theory, each accessing its forcing extensions; with rank potentialism, one considers the collection of of rank-initial segments $V_\alpha$ of a given set-theoretic universe; with Grothendieck–Zermelo potentialism, one has the collection of $V_\kappa$ for (a proper class of) inaccessible cardinals $\kappa$; with top-extensional potentialism, one considers the collection of countable models of ZFC under the top-extension relation; and so on with many other natural examples.

In this tutorial, we shall settle the precise potentialist validities of each of these potentialist systems and others, and we shall develop the general tools that enable one to determine the modal theory of a given potentialist system. Many of these arguments proceed by building connections between certain sweeping general features of the models in the potentialist system and certain finite combinatorial objects such as trees or lattices. A key step involves finding certain kinds of independent control statements — buttons, switches, ratchets and rail-switches — in the collection of models.

slides

# Research Track

SpeakerTitleAbstract/Slides
Viera ŠottováwQN-space and ideal coverings of X slides
Taras BanakhA parallel metrization theoremabstract slides
Serhii BardylaOn locally compact semitopological graph inverse semigroupsabstract slides
Adam BartošCompactifiability and Borel complexity up to equivalenceabstract slides
Wojciech BielasSeparation axiom for regular closed sets slides
Andrew Brooke-TaylorProducts of CW complexesabstract slides
Noé de RancourtApproximate Gowers spaces slides
Stamatis DimopoulosCardinal characteristics and strong compactnessabstract slides
Monroe EskewRigid collapseabstract slides
Saeed GhasemiAlmost disjoint families and C*-algebrasabstract slides
Michał Tomasz GodziszewskiTruth theories and satisfaction classes over models of set theory slides
Martin GoldsternCichoń's Maximumabstract slides
Miha HabičSurgery and nonamalgability for Cohen reals slides
Eliza JabłońskaOn Steinhaus properties and families of "small" sets slides
Asaf KaragilaTBD slides
Olena KarlovaAlmost strongly zero-dimensional spacesabstract
Michał KorchSpecial subsets of the generalized Cantor space $2^\kappa$abstract slides
Ziemowit KostanaNon-measurability of the algebraic sums of sets of real numbersabstract slides
Wieslaw KubisThe weak amalgamation property slides
Ondřej KurkaLarge separated sets of unit vectors in Banach spaces of continuous functionsabstract slides
Marta KwelaIdeals of nowhere dense sets in some topologies on integers slides
Maxwell LevineForcing Square Sequencesabstract slides
Marcin MichalskiLuzin and Sierpiński sets meet treesabstract slides
Heike MildenbergerBlock Sequences with Projections into a Sequence of Happy Familiesabstract slides
Kaethe MindenSubcomplete Forcing, Trees, and Generic Absoluteness slides
Volodymyr MykhaylyukUpper Namioka property of multi-valued mappingsabstract slides
Grzegorz PlebanekMardesic problem on products of compact lines slides
Robert RałowskiNonmeasurable images in Polish space with respect to $\sigma$-ideals with Borel base slides
Jonathan SchilhanThe generalized meager ideal and clubs slides
Olga SipachevaBoolean topological groups and ultrafiltersabstract slides
Damian SobotaGrothendieck C(K)-spaces of small densityabstract slides
Filip StrobinCompact scattered spaces as attractors of generalized IFSsabstract slides
Jaroslav SupinaCardinal characteristic of ideals and three selection principles slides
Jarosław SwaczynaHaar-small sets slides
Jonathan VernerThe Last Talk slides
Alessandro VignatiTriviality and nontriviality of homeomorphisms of Čech–Stone remaindersabstract slides
Thilo WeinertThoughts on density pointsabstract slides
Wolfgang WohofskyNon-stationary topology on $2^\kappa$abstract slides
Shuguo ZhangA non-Hurewicz set of reals of size $\mathfrak d$ with all its powers Menger slides