## 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…

## Teoria dei modelli della doppia appartenenza – Rosario Mennuni

È facile mostrare che il “grafo di appartenenza” di ogni modello numerabile della teoria degli insiemi, ottenuto collegando x e y se x appartiene a y *oppure* y appartiene a x, è isomorfo al Grafo Random (o Grafo di Rado). Questo è vero per teorie…

## Stably embedded ordered abelian groups – Pierre Touchard (Università degli Studi della Campania “Luigi Vanvitelli”)

It is well known that in a stable theory, all types are definable. In an unstable context, we can ask (like Cubides and Delon in [CD]) over which models $M$ of a given theory all types are definable. These models are exactly the models which are…

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