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.

    Publications supported by the project

  • D. García. Ordered asymptotic classes of finite structures. In preparation.
  • D. García. Model theory of pseudofinite structures. In preparation. Lecture Notes.

    Talks supported by the project:

    1. The Erdös-Hajnal conjecture for stable graphs. [notes]
      School of Mathematics. University of Manchester.
    2. Applications of ultraproducts of finite structures to combinatorics. [abstract]
      Institute for Research in Fundamental Sciences. Isfahan, Iran.
    3. Unimodularity unified. [slides]
      Logic Colloquium 2016. University of Leeds.
    4. O-asymptotic classes of finite structures. Model Theory Seminar. University of Leeds.
    5. Pseudofinite structures and simplicity. Logic Seminar. University of Oxford.
    6. Lancashire Yorkshire Model Theory Seminar - LYMOTS.

    Conference participation supported by the project:

    1. Model Theory and applications to Geometry. Universita deli study di Padova. Italy.
    2. Model Theory, Bedlewo. Banach Center - Institute of Mathematics. Poland.
    3. Model Theory in Wroclaw. Instytut Matematyczny Univerwsytet Wroclawski, Wroclaw, Poland.
    4. Model Theory and Applications. University&‌eacute; de Mons, Belgium.
    5. Chernin weekend. Rutgers University, NJ, USA.