Skip to main content
Un sito ufficiale dell’Unione europeaUn sito ufficiale dell’UE
European Commission logo
italiano italiano
CORDIS - Risultati della ricerca dell’UE
CORDIS
CORDIS Web 30th anniversary CORDIS Web 30th anniversary

Model theory of finite and pseudofinite structures

Obiettivo

The project is in model theory (mathematical logic), which concerns the expressibility in logical languages of properties of mathematical structures (e.g. graphs, groups, rings). Model theory aims to identify borders between `tame' and `wild' objects in mathematics, and to pin down abstract notions of independence and dimension and understand the geometry of `definable sets' in a structure, often with wide-ranging applications. This project focusses on classes of finite structures (e.g. the class of all finite fields), and on the `ultraproduct' construction which converts a class of finite structures to an infinite `pseudofinite' structure' which inherits properties of the class and is amenable to model-theoretic methods, with applications for the finite structures. Key objectives include:
(i) proving a trichotomy for pseudofinite geometries -- they should be `trivial', `group-like', or `field-like';
(ii) developing current concepts from abstract model theory for pseudofinite structures;
(iii) identifying first order properties of pseudofinite groups, and constraints on their possible quotients;
(iv) finding links between the model-theoretic `independence theorem', Gowers' notion of `quasi-random groups', and the Szemeredi regularity theorem in graph theory.
(v) model theory of finite ordered structures, and links to finite model theory.

To support his future academic research career, the Fellow, Garcia, will receive training through research in the model theory groups in Leeds and (through a secondment) Lyon. There will be knowledge transfer to Garcia of expertise in model-theoretic algebra of Leeds and Lyon, and Garcia will also build knowledge of finite model theory and its computer science applications. He will receive complementary training in many research skills (including outreach), and will transfer to Leeds expertise he has gained in the excellent model theory groups in Berkeley and Bogota, while deepening EU-Colombia mathematics links.

Meccanismo di finanziamento

MSCA-IF-EF-ST - Standard EF

Coordinatore

UNIVERSITY OF LEEDS
Contribution nette de l'UE
€ 183 454,80
Indirizzo
WOODHOUSE LANE
LS2 9JT Leeds
Regno Unito

Mostra sulla mappa

Regione
Yorkshire and the Humber West Yorkshire Leeds
Tipo di attività
Higher or Secondary Education Establishments
Collegamenti
Costo totale
€ 183 454,80