Research Training Network in Model Theory
Publications > Introductory Notes and surveys

Introductory Notes and Surveys

Introductory notes
  • Luc Bélair, Panorama of p-adic model theory, Ann. Sci. Math. Québec. A survey of the literature in the model theory of p-adic numbers since Denef's work on the rationality of Poincaré series.
  • Enrique Casanovas Groups in stable and simple theories (April 2006). A few results, maybe not well-known, on bounded type-definable relations and canonical bases.
  • Zoé Chatzidakis
    • Introduction to model theory (26 pages, format dvi). These notes introduce very basic concepts of model theory. They contain some of the material of lectures given at Luminy (November 01).
    • Notes on the model theory of finite and pseudo-finite fields (45 pages, format dvi or ps). These notes contain the material covered during a mini-course which took place at the UAM (Madrid, Spain), 15 - 25 November 2005, and was funded by MODNET.
  • Artem Chernikov
  • Michel Coste
  • Adrien Deloro
    • Groups of finite Morley rank and their representations. Notes for a mini-course given at Universidad de los Andes in May 2017 (revised May 2019). There were four lectures of 105 minutes each, although 2 hours might have been more reasonable.
    • Groups of small Morley Rank. Notes for a mini-course given at Universidad de los Andes in October 2018. There were five lectures of two hours each, devoted to proving the Cherlin-Zilber conjecture in rank 3 (32 pages).
  • Margarita Otero, A survey on groups definable in o-minimal structures (30 pages, format pdf).
  • Ya'acov Peterzil, A self-guide to o-minimality (notes for a tutorial given in the Camerino Summer School, June 2007).
  • Anand Pillay, Lecture notes from a recent sequence of courses in model theory:
  • A. J. Wilkie, Lectures on elimination theory for semialgebraic and subanalytic sets. Notes from courses given at UI Chicago and at Notre Dame, fall 2010.
  • Boris Zilber, Lecture notes from graduate courses.
    • Elements of Geometric Stability Theory (48 pages, ps)
    • Zariski Geometries (85 pages, dvi, ps, pdf)
  • Lecture notes from the Leeds MODNET summer school (12 - 17 December 05).
  • Lecture notes from the MODNET Summer School 2007, Camerino, 14 - 16 June 2007.
    • Model Theory of Groups (Andreas Baudisch, Humboldt-Universität Berlin). Slides.
    • Model Theory of Modules (Philipp Rothmaler, CUNY). Paper.
    • Introduction to o-minimality (Kobi Peterzil, U. of Haifa). Notes.
  • Lecture notes from the MODNET Research Workshop, Humboldt-Universität Berlin, 10-14 September 2007. Notes on the courses.
    • Model Theory of Fields (Françoise Delon, Université Paris 7)
    • O-minimality, Part II. On the construction of o-minimal structures (Alex Wilkie, The University of Manchester). Notes by participants.
    • Applications of Model Theory of Fields. The Zariski dichotomy and Mordell-Lang (Rahim Moosa, University of Waterloo). Notes by participants.
  • Lecture notes from the La Roche MODNET Training Workshop Model theory and Applications, 20 - 25 April 2008. Notes on the tutorials written by students and post-docs.
References of some survey papers
  • Anand Pillay, Model theory, Notices Amer. Math. Soc. 47 (2000), no. 11, 1373 - 1381.
  • Anand Pillay, Model theory and stability theory, with applications in differential algebra and algebraic geometry, in: Model theory with applications to algebra and analysis. Vol. 1, 1 - 23, London Math. Soc. Lecture Note Ser., 349, Cambridge Univ. Press, Cambridge, 2008.
  • Rahim Moosa, Model theory and complex geometry, Notices Amer. Math. Soc. 57 (2010), no. 2, 230 - 235.
  • Thomas Scanlon, Counting special points: Logic, diophantine geometry, and transcendence theory, Bull. Amer. Math. Soc. (N.S.) 49 (2012), no. 1, 51 - 71.

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