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…
Categoria evento: Logic Seminar
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…
Central Sets and infinite monochromatic exponential patterns – Mariaclara Ragosta (Università di Pisa)
Schur’s Theorem (1916) states that for every finite coloring of $\mathbb N$ there exists a monochromatic triple $a, b, a+b$. Several decades passed before Folkman and Sanders extended this statement from two integers $a, b$ to arbitrarily long…
On the classification problem of countable abelian groups – Martino Lupini (Università di Bologna)
I will present the framework of Borel-definable homological algebra, where classical constructions and invariants from homological algebra are enriched with additional information of descriptive set-theoretic nature. I will then explain how this…
Collinearity on cubic surfaces – Jan Dobrowolski (University of Manchester)
We study the ternary relation R of collinearity between points of a smooth cubic surface X. Our aim is to understand sequences of triples (A,B,C) of finite sets with |A|=|B|=|C| whose Cartesian products have asymptotically maximal possible size of…
Infinity-categories and infinity-operads – Francesca Pratali (Université Sorbonne Paris Nord)
An operad is a structure that consists of abstract operations, each one having a fixed finite number of inputs and one output, as well as maps defining composition laws. A coloured operad is an operad where input elements and the output are allowed…
Modelli booleani e come fascificarli – Moreno Pierobon (Università di Pisa)
I modelli booleani sono strutture in cui i valori di verità degli enunciati sono elementi di un’algebra di Boole (tipicamente infinita). Nati come approccio alla tecnica del forcing, essi sono anche un valido strumento per costruire nuove strutture…