Modnet
Model Theory Network

Introductory Notes and Surveys

This section will be updated shortly.

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, pdf). 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
  • Lecture Notes on Stability Theory (Winter 2015, UCLA. 52 pages)
  • Topics in combinatorics (Winter 2016, UCLA. 48 pages)
• Michel Coste
  • An Introduction to Semialgebraic Geometry (77 pages)
  • An Introduction to O-minimal Geometry (82 pages)
• 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).
• Christian d'Elbée, Axiomatic Theory of Independence Relations in Model Theory, 53 pages. These notes originate from a neostability course held during the summer semester of 2023 at the University of Bonn.
• Isaac Goldbring and Bradd Hart, A survey on the model theory of tracial von Neumann algebras. We survey the developments in the model theory of tracial von Neumann algebras that have taken place in the last fifteen years.
• Bradd Hart, An Introduction To Continuous Model Theory. (53 pages; first draft; comments welcome; to appear in the volume Model theory of operator algebras as part of DeGruyter's Logic and its Application Series). We present an introduction to modern continuous model theory with an emphasis on its interactions with topics covered in this volume such as $C^*$-algebras and von Neumann algebras. The role of ultraproducts is highlighted and expositions of definable sets, imaginaries, quantifier elimination and separable categoricity are included.
• Rahim Moosa, Six lectures on model theory and differential-algebraic geometry. Write up of lectures given at the Field Institute in Toronto, during the programme Trends in Pure and Applied Model Theory, Fall 2021.
• Margarita Otero, A survey on groups definable in o-minimal structures (30 pages).
• 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:
  • Model Theory (61 pages), Fall 2002
  • Stability Theory (73 pages), Spring 2003
  • Applied Stability Theory (49 pages), Fall 2003
• 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).
  • Eric Jaligot, Introduction to Stability Theory: Part I (pdf) (A. Amantini), Part II (pdf) (J. Potier).
  • Angus Macintyre, Algebra and Geometry (J. Caycedo, F. Maalouf).
  • Mike Prest, Intermediate Model Theory (J. de la Rue, M. Ferreira).
• 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.
  • Tutorial Geometric motivic integration by R. Cluckers: Part I (M. Kamensky), Part 2 (C. Milliet), Part 3 (A. Chernikov).
  • Tutorial Model Theory of Valued fields by D. Macpherson (N. Frohn, G. Onay, R. De Aldama and O. Roche).
  • Tutorial On Interactions between Model theory and number theory (Galois groups and transcendence) by D. Bertrand, P. Kowalski and A. Pillay.
    • Introduction to the Ax-Schanuel property (C. Berthet)
    • The Lindemann-Weierstrass theorem for semi-abelian varieties over function fields (G. Giabicani)
    • An extension of the Lindemann-Weierstrass theorem (A. Peón Nieto)
  • Tutorial Finite model theory by A. Dawar

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.