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…
Categoria evento: Logic Seminar
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…