Soutenance de thèse : Aliaume Lopez

Sep 12 14:00 ₂₀₂₃

Preservation Theorems in first-order logic are a collection of results derived from classical Model Theory. These results establish a direct correspondence between the semantic properties of formulas and the syntactic constraints imposed on the language used to express them. However, studying these theorems becomes notably challenging when focusing on finite models, which is unfortunate given that the field of Finite Model Theory is better equipped to describe phenomena occurring in Computer Science. This thesis presents a systematic approach to investigating Preservation Theorems within the realm of Finite Model Theory. The traditional ad-hoc proofs are replaced with a theoretical framework that generalizes techniques based on locality, and introduces a topological presentation of preservation theorems called logically presented pre-spectral spaces. Introducing these topological spaces enables the development of a compositional theory for preservation theorems. Additionally, this thesis takes an initial stride towards systematically examining preservation theorems across inductively defined classes of finite structures. It accomplishes this by proving a generic fixed point theorem for a topological restriction of logically presented pre-spectral spaces, specifically Noetherian spaces.

Directrice de thèse et encadrantes :

• Jean Goubault-Larrecq, Professeur des universités, LMF, CNRS, Université Paris Saclay - Directeur de thèse
• Sylvain Schmitz, Professeur des universités, IRIF, Université Paris-Cité - Co-encadrant de thèse

Jury:

• Serenella Cerrito, Professeure des Universités, Université Paris Saclay, Univ EVRY, France
• Anuj Dawar, Professor, University of Cambridge
• Arnaud Durand, Professeur des Universités, Université Paris-Cité
• Patrice Ossona de Mendez, Chargé de Recherche, EHESS
• Daniela Petrisan, Maîtresse de Conférences, Université Paris-Cité
• Luca Reggio, Senior Fellow Researcher, University College London