A sessionwise schedule for readings is provided in the table below.
References
Ben-Yaacov, Itay. "Positive Model Theory and Compact Abstract Theories." Journal of Mathematical Logic 3, no. 1 (2003): 85–118.
Ben-Yaacov, Itay. "Simplicity in Compact Abstract Theories." Journal of Mathematical Logic 3, no. 2 (2003): 163–191.
Ben-Yaacov, Itay. "Thickness, and a Categoric View of Type-space Functors." Fundamenta Mathematicae 179 (2003): 199–224.
Ben-Yaacov, Itay. "Lovely Pairs of Models: The Non First Order Case." Journal of Symbolic Logic 69, no. 3 (2004): 641–662.
Chatzidakis, Zoë, and Anand Pillay. "Generic Structures and Simple Theories." Annals of Pure and Applied Logic 95 (1998): 71–92.
Kim, Byunghan. "Forking in Simple Unstable Theories." Journal of the London Mathematical Society 57, no. 2 (1998): 257–267.
Kim, Byunghan. "A Note on Lascar Strong Types in Simple Theories." Journal of Symbolic Logic 63, no. 3 (1998): 926–936.
Kim, Byunghan, and Anand Pillay. "Simple Theories." Annals of Pure and Applied Logic 88 (1997): 149–164.
Pillay, Anand. "Forking in the Category of Existentially Closed Structures." In Connections between Model Theory and Algebraic and Analytic Geometry. Edited by Angus Macintyre. Vol. 6, Quaderni di Matematica. University of Naples, 2000.
Wagner, Frank O. Simple Theories. Vol. 503. Mathematics and its Applications. Dordrecht, NL: Kluwer Academic Publishers, 2000. ISBN: 0792362217.
General References
General First Order Simplicity Theory
Wagner, Frank O. Simple Theories. Vol. 503. Mathematics and its Applications. Dordrecht, NL: Kluwer Academic Publishers, 2000. ISBN: 0792362217.
The original development appears in the following three readings:
Kim, Byunghan. "Forking in Simple Unstable Theories." Journal of the London Mathematical Society 57, no. 2 (1998): 257–267.
Kim, Byunghan, and Anand Pillay. "Simple Theories." Annals of Pure and Applied Logic 88 (1997): 149–164.
Kim, Byunghan. "A Note on Lascar Strong Types in Simple Theories." Journal of Symbolic Logic 63, no. 3 (1998): 926–936.
Development of Simplicity in Compact Abstract Theories (without Assuming Thickness or Extension)
Ben-Yaacov, Itay. "Simplicity in Compact Abstract Theories." Journal of Mathematical Logic 3, no. 2 (2003): 163–191.
The development presented in the course is closer to that of Anand Pillay's "Forking in the Category of Existentially Closed Structures." (although the model-theoretic setting is slightly different)
Readings by Session
| SES # | TOPICS | READINGS |
|---|---|---|
| 1 | The Basic Setting: Universal Domains | Ben-Yaacov, Itay. "Positive Model Theory and Compact Abstract Theories." Journal of Mathematical Logic 3, no. 1 (2003): 85–118. |
| 2 | Extraction of Indiscernible Sequences (Taught by David K. Milovich) |
|
| 3 | Dividing and its Basic Properties | |
| 4 | Simplicity Statement of the Properties of Independence Morley Sequences Proof of Symmetry and Transitivity from Extension |
|
| 5 | Thickness Total D-rank and Extension |
Ben-Yaacov, Itay. "Thickness, and A Categoric View of Type-space Functors." Fundamenta Mathematicae 179 (2003): 199–224. |
| 6 | Lascar Strong Types and the Independence Theorem (Partially taught by Christina Goddard) |
Ben-Yaacov, Itay. "Simplicity in Compact Abstract Theories." Journal of Mathematical Logic 3, no. 2 (2003): 163–191. Or, Pillay, Anand. "Forking in the Category of Existentially Closed Structures." In Connections between Model Theory and Algebraic and Analytic Geometry. Edited by Angus Macintyre. Vol. 6, Quaderni di Matematica. University of Naples, 2000. |
| 7 | Examples: Hilbert Spaces, Hyperimaginary Sorts (Taught by Josh Nichols-Barrer) |
|
| 8 | Generically Transitive Relations Amalgamation Bases, Parallelism and Canonical Bases |
|
| 9 | Characterisation of Simplicity and Non-dividing in Terms of Abstract Notion of Independence (Taught by Cameron Freer) |
|
| 10 | Supersimplicity Lascar Inequalities Stability |
|
| 11-12 | Stable Theories with a Generic Automorphism | Chatzidakis, Zoë, and Anand Pillay. "Generic Structures and Simple Theories." Annals of Pure and Applied Logic 95 (1998): 71–92. |
| 13-14 | Groups: Stratified Ranks, Generic Elements and Types Connected Components, Stabilisers |
|
| 15-16 | Lovely Pairs | Ben-Yaacov, Itay. "Lovely Pairs of Models: The Non First Order Case." Journal of Symbolic Logic 69, no. 3 (2004): 641–662. |