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 $G×G$ contains an corner.…
Categoria evento: Logic Seminar
Model completeness of finitely ramified henselian valued fields with various value groups – Anna De Mase (Università della Campania “Luigi Vanvitelli”)
A result obtained by A. Macintyre and J. Derakhshan states that the theory of a mixed characteristic henselian valued field with finite ramification, perfect residue field and whose value group is a Z-group, is model complete in the language of…
Gruppi con topologia di Zariski cofinita – Dikran Dikranjan (Università di Udine)
La topologia di Zariski ${\mathfrak Z}_G$ di un gruppo $G$, fu introdotta esplictamente da R. Bryant [2] sotto il nome verbal topology, ma implicitamente suggerita da Markov [6]. I sottoinsiemi di $G$ della forma $\{x\in G: g_1 x^{\varepsilon_1} g_2…
Quasiminimality of complex powers – Francesco Gallinaro (Albert-Ludwigs-Universität Freiburg)
A conjecture due to Zilber predicts that the complex exponential field is quasiminimal: that is, that all subsets of the complex numbers that are definable in the language of rings expanded by a symbol for the complex exponential function are…
Projective Absoluteness from Strong Cardinals – Cesare Straffelini (Universitat de Barcelona)
We will give a proof of an unpublished theorem by Hugh Woodin, which states that if there is a proper class of strong cardinals, then by Lévy collapsing the universe we can find a model of ZFC which is projective absolute under set forcing. This,…
First-order aspects of Coxeter groups – Gianluca Paolini (Università di Torino)
We will talk about recent advancement on the model theory of Coxeter groups. We will focus in particular on affine Coxeter groups and on Droms right-angled Coxeter groups. These investigations lead to a general model-theoretic analysis of…
Combinatorial statements from a compact right topological semigroup of types – Claudio Agostini (TU Wien)
Many theorems in combinatorics share a very similar structure: Let $M$ be monoid acting by endomorphism on a partial semigroup $S$. For each finite coloring of $S$, there are “nice” monochromatic subsets $N\subseteq S$. Examples of theorems of…
A Feferman Vaught theorem for products of commutative unital rings – Paola D’Aquino (Università degli studi della Campania “Luigi Vanvitelli”)
We axiomatize the class of commutative unital rings which are elementarily equivalent to a non trivial product of commutative unital connected rings, obtaining in this way a converse of the classical result of Feferman and Vaught for the class of…
A limiting result for the partition regularity of functional equations – Paulo Arruda (Universität Wien)
Our main result provides a condition under which the partition regularity (PR) of systems of functional equations over a given infinite set can be completely characterised by the existence of constant solutions. From this result, we characterise the…
An unbounded version of Zarankiewicz’s problem – Pantelis Eleftheriou (University of Leeds)
Zarankiewicz’s problem for hypergraphs asks for upper bounds on the number of edges of a hypergraph that has no complete sub-hypergraphs of a given size. Let M be an o-minimal structure. Basit-Chernikov-Starchenko-Tao-Tran (2021) proved that the…