EU project 656422 - MODFIN

Basic information

  • Hosting institution: University of Leeds

  • Project supervisor: Dugald MacPherson,

  • Researcher: Darío García,

  • Project period: 01.06.2016 - 31.05.2018

  • Summary of the project

    The project concerns the interplay between model theory of finite structures (in the sense of first order logic) and their infinite limits (pseudofinite structures, e.g. ultraproducts). Our objectives are clustered into three main themes, namely: to develop modern model-theoretic techniques of generalized stability theory in the context of pseudofinite structures; to develop the theory of pseudofinite groups, with connections to Szemeredi’s Regularity Theorem, and to build a model theory of (pseudo)finite ordered structures and explore links to finite model theory, a topic in theoretical computer science.

    Project Conference

    In the context of the this project, we organised the Workshop on Finite and Pseudofinite Structures (FPS-2018) which was held at the School of Mathematics of the University of Leeds.

    The programme comprised a total of 15 lectures (5 of them given by female speakers), which reflected the variety of topics in the subject: asymptotic classes and measurable structures, ω- categorical and homogeneous structures, pseudofinite groups and fields, and some lectures about the novel topic of pseudofinite structures in continuous logic due to Isaac Goldbring and Aleksander Ivanov.

    For information about the programme (including the slides for several talks) are available here . More information about this workshop can be found in the official webpage of the event.

    Publications supported by the project

  • D. García. Ordered asymptotic classes of finite structures. Submitted. Preprint.

  • D. García. Model theory of pseudofinite structures. In preparation. Lecture Notes.

    Talks supported by the project:

    1. Forking and thorn-forking for generically stable types [ slides]
      Logic Seminar. University of Leeds.

    2. Minicourse on model theory of pseudofinite structures. [ Notes.]
      Trimester programme Model Theory, Valued Fields and Combinatorics . Institut Henri Poincaré.

    3. Pseudofinite structures, simplicity and unimodularity [slides ]
      Rencontres franco-colombiennes des mathématiques. Ecole Normale Superiure, Lyon. France.

    4. Ordered asymptotic classes of finite structures [handout ]
      Logic Seminar. Imperial College - London.

    5. Furstenberg principle via ultraproducts of finite structures.
      Mathematisches Institut. University of Freiburg.

    6. Ultraproducts of finite structures in combinatorics. [slides ]
      Birkbeck College, University of London.

    7. The Erdös-Hajnal conjecture for stable graphs. [notes]
      School of Mathematics. University of Manchester.

    8. Forking and dimensions in pseudofinite structures [slides]
      Logic Seminar. University of Leeds.

    9. Applications of ultraproducts of finite structures to combinatorics. [abstract] Institute for Research in Fundamental Sciences. Isfahan, Iran.

    10. Unimodularity unified. [slides]
      Logic Colloquium 2016. University of Leeds.

    11. O-asymptotic classes of finite structures. Model Theory Seminar. University of Leeds.

    12. Pseudofinite structures and simplicity. Logic Seminar. University of Oxford.

    13. Lancashire Yorkshire Model Theory Seminar - LYMOTS.

    Conference participation supported by the project:

    1. Set theory, Model theory and applications.   Research Workshop held at the Eilat Campus of Ben-Gurion University of the Negev. Israel.

    2. Model Theory, Combinatorics and Valued Fields. Trimester programme at the Institute Henri Poincaré.

    3. Model Theory and applications to Geometry. Università degli study di Padova. Italy.

    4. Model Theory, Bedlewo. Banach Center - Institute of Mathematics. Poland.

    5. Model Theory in Wroclaw. Instytut Matematyczny Univerwsytet Wroclawski, Wroclaw, Poland.

    6. Model Theory and Applications. Université de Mons, Belgium.

    7. Cherlin weekend. Rutgers University, NJ, USA.

    Outreach activities supported by the project:

    As part of the Marie Curie outreach dissemination activities, I organised the workshop "Colors and Paths" for students at the Airedale Academy in Castleford, and the Buttershaw Business and Enterprise College in Bradford. See the handout of the activity here. Pictures coming soon!