A long outstanding conjecture is that every infinite stable field is separably closed. The class of

I will begin with an introduction to stable groups, discuss earlier work done on stable fields and review the necessary background on large fields.

I plan to give one lecture/week on Zoom, Each session will be at most 75 minutes, but more likely an hour or less. Please contact me (marker@uic.edu) if you need the Zoom link.

The chapter of my text on omega-stable groups is also useful background.

- A. Chernikov, Lectures on Stability Theory
- F. Delon, Separably closed fields,
*Model theory and algebraic geometry*, E. Bouscaren ed., Lecture Notes in Math., 1696, Springer, 1998. - J.-L. Duret, Les corps faiblement algébriquement clos non séparablement clos ont la propriété d'indépendence, {\em Model theory of algebra and arithmetic}, pp. 136–162, Lecture Notes in Math., 834, Springer, Berlin-New York, 1980.
- Y. Halevei, A. Hasson and, F. Jahnke, Definable V-topologies, henselianity and NIP, J. Math. Log. 20 (2020), no. 2, 2050008, 33 pp.
- W. Johnson, C-M. Tran, E. Walsberg and J.Ye, Etale open topology and the stable field conjecture
- I. Kaplan, T. Scanlon and F. Wagner, Artin-Schreier extensions in NIP and simple fields, Israel J. Math. 185 (2011), 141--153.
- D. Marker,
*Model Theory: An Introduction*, Springer, 2002. - D. Marker, Lecture Notes on Model Theory of Valued Fields Fall 2018.
- M. Messmer, Some model theory of separably closed fields,
*Model theory of fields*, D. Marker, M. Messmer, A.Pillay ed., Lecture Notes in Logic, 5. Association for Symbolic Logic, A. K. Peters, 2006. - A. Pillay and E. Walsberg, Galois groups of large simple fields
- B. Poizat, Groupes stables, avec types génériques réguliers, J. Symbolic Logic 48 (1983), no. 2, 339--355.
- B. Poizat,
*Stable Groups*, AMS, 2001. - F. Pop, Embedding problems over large fields. Ann. of Math. (2) 144 (1996), no. 1, 1--34.
- F. Pop, Little survey on large fields
- A. Prestel and M. Ziegler, Model-theoretic methods in the theory of topological fields. J. Reine Angew. Math. 299(300) (1978), 318–341.
- T. Scanlon, Infinite stable fields are Artin--Schrier closed
- K. Tent and M. Ziegler,
*A Course in Model Theory*, Cambridge University Press, 2012 - E. Walsberg, Topological approach to the theory of large fields?, in progress.

- Lecture 1 Introduction + chain conditions in stable groups
- Lecture 2 generic types in stable groups
- Lecture 3 more on generic types in stable groups
- Lecture 4 stable fields
- Lecture 5 large stable fields
- Lecture 6 the etale open topology

Last Revised: 3/15/21