Tuesday,
20211109
14:30

Raum 404, ErnstZermeloStr. 1
Giorgio Laguzzi:
Construction and Representation of Generalised Equitable Preference Relations (Based on a Joint Paper with Ram Sewak Dubey)
In recent years a strict connection between set theory and social welfare relations has been studied in theoretical economics. In this talk I present some generalised versions of redistributional equity principles for infinite populations. More specifically we focus on the representation and construction of social welfare relations satisfying these generalised principles and we also combine them with other known efficiency and intergenerational equity principles in economic theory; in particular, important roles from set theory are played by ultrafilters and nonRamsey sets. 
Tuesday,
20211116
14:30

Raum 404, ErnstZermeloStr. 1
Rémi Jaoui:
The number of models of the theory of existentially closed differential fields revisited.
In 1973, Shelah showed that the theory of existentially closed differential fields of characteristic 0 although complete and totally transcendental admits the maximal number of models in any uncountable cardinality. This was extended by HrushovskiSokolovic and independently by Pillay to countable models in the 90’s.
In my talk, I will discuss how to recover (local and global versions of) Shelah’s result from the study of a specific family of differential equations: the differential equations of the form y’’/y’ = f(y) where f(y) is an arbitrary rational function introduced by Poizat in the 90's.
This is joint work with J. Freitag, D. Marker and R. Nagloo. 
Tuesday,
20211123
14:45

Raum 404, ErnstZermeloStr. 1
Amador Martin Pizarro:
On abelian corners and squares
Given an abelian group G, a corner is a a subset of pairs of the form ${(x,y), (x+g, y), (x, y+g)}$ with $g$ non trivial. Ajtai and Szemerédi proved that, asymptotically for finite abelian groups, every dense subset $S$ of $G\times G$ contains an corner. Shkredov gave a quantitative lower bound on the density of the subset $S$. In this talk, we will explain how modeltheoretic conditions on the subset $S$, such as local stability, will imply the existence of corners and of cubes for (pseudo)finite abelian groups. This is joint work with D. Palacin (Madrid/Freiburg) and J. Wolf (Cambridge). 
Tuesday,
20211130
14:30

Raum 404, ErnstZermeloStr. 1
Maxwell Levine:
On the Distributivity of Perfect Tree Forcings for Singulars of Uncountable Cofinality
Forcing with perfect trees is a major topic of research in set theory. One example is Namba forcing, which was originally developed as an example of a forcing that is $(\aleph_0,\aleph_1)$distributive but not
$(\aleph_0,\aleph_2)$distributive. A recent paper of Dobrinen, Hathaway, and Prikry shows that a classical singular Namba forcing
$P_\kappa$ is $(\omega,\nu)$distributive for $\nu<\kappa$ if $\kappa$ is a singular strong limit cardinal of countable cofinality. The authors then ask whether this result generalizes, i.e. if
$P_\kappa$ is (cf$(\kappa),\nu)$distributive for $\nu<\kappa$ if $\kappa$ has uncountable cofinality. In joint work with Heike Mildenberger, we answer this question in the negative by showing that in this case
$P_\kappa$ is not (cf$(\kappa),2)$distributive. 
Tuesday,
20211207
14:30

Raum 404, ErnstZermeloStr. 1
Michael Lösch:
On the canonical base property and transfer of internality
Baldwin and Lachlan proved that an uncountably categorical structure is largely controlled by a strongly minimal set D and the Canonical Base Property (CBP) states that over a realization of a stationary type, its canonical base is always almost internal to the strongly minimal set D.
Chatzidakis, Moosa and Pillay showed under the assumption of the CBP that every almost Dinternal type transfers internality on intersections and more generally on quotients. Both properties do not hold in the uncountably categorical structure without the CBP, produced by Hrushovski, Palacín and Pillay.
In this talk, I will show that transfer of internality of quotients already implies the CBP and present the counterexample to the CBP as an additive cover of the complex numbers. In order to show that this structure does not transfer internality, we must consider imaginary elements (definable equivalence classes) and obtain a connection between elimination of finite imaginaries and the failure of the CBP. 
Tuesday,
20220118
14:3016:00

Raum 404, ErnstZermeloStr. 1
Martin Bays (Universität Münster):
Density of compressibility
Compressibility is a certain isolation notion suited to NIP theories. One definition of distality of a theory (a crucial notion with useful combinatorial consequences) is that every type is compressible. I will discuss some good properties of compressibility and their consequences, which include the existence of "compressibly atomic" models over arbitrary sets in countable NIP theories, and uniform honest definitions for an NIP formula.
Joint work with Itay Kaplan and Pierre Simon. 
Tuesday,
20220125
14:3016:00

Raum 404, ErnstZermeloStr. 1
Leon Chini:
DistalityRank
For 1≤k<ω we introduce kdistality and strong kdistality as properties of firstorder theories, which both coincide with distality for k=1. With these properties we define the (strong) distality rank of a theory, and we give examples of theories with (strong) distality rank m for all ordinal numbers m between 1 and ω. We prove that the two ranks coincide for strongly minimal theories by providing a characterization in terms of the algebraic closure. 
Tuesday,
20220201
14:3016:00

Raum 404, ErnstZermeloStr. 1
Maja König:
Der Satz von Lindström
Der Satz von Lindström charakterisiert die Prädikatenlogik erster Stufe
als stärkste Logik, in welcher der Kompaktheitssatz und der Satz von
LöwenheimSkolem abwärts gelten. Um den Satz sauber formulieren zu
können, muss zunächst geklärt werden, was unter einer Logik zu
verstehen ist. Hierzu wird in diesem Vortrag der von Chang und Keisler
eingeführte Begriff einer abstrakten Logik diskutiert. Anschließend
kann der Satz von Lindström präzise formuliert und bewiesen werden. Im
Beweis, der sich ebenfalls am Vorgehen von Chang und Keisler
orientiert, wird die Charakterisierung von elementarer Äquivalenz
mithilfe von BackandForth Systemen eine wichtige Rolle spielen. 
Tuesday,
20220208
14:3016:00

Raum 404, ErnstZermeloStr. 1
Ulla Karhumäki:
Small groups of finite Morley rank with a supertight automorphism
The famous CherlinZilber Algebraicity conjecture proposes that any infinite simple $\aleph_1$categorical group is isomorphic to a simple algebraic group over an algebraically closed field.
In my talk, I will first explain the current state of the CherlinZilber conjecture. I will then introduce a recent approach towards this conjecture, which is based on the notion of a supertight automorphism. I will discuss a result, proven jointly with P. Ugurlu, on “small” infinite simple groups of finite Morley rank with a supertight automorphism whose fixedpoint subgroup is pseudofinite. 