everything.study
18.996A

Simplicity Theory

Graduate · Historical course

Spring 2004

Topics

  • The Basic Setting: Universal Domains
  • Extraction of Indiscernible Sequences (Taught by David K. Milovich)
  • Dividing and its Basic Properties
  • Simplicity
  • Thickness
  • Lascar Strong Types and the Independence Theorem (Partially taught by Christina Goddard)
  • Examples: Hilbert Spaces, Hyperimaginary Sorts (Taught by Josh Nichols-Barrer)
  • Generically Transitive Relations
  • Characterisation of Simplicity and Non-dividing in Terms of Abstract Notion of Independence (Taught by Cameron Freer)
  • Supersimplicity
  • Stable Theories with a Generic Automorphism
  • Groups: Stratified Ranks, Generic Elements and Types
  • Lovely Pairs

Readings

  • Ben-Yaacov, Itay. “Positive Model Theory and Compact Abstract Theories.” Journal of Mathematical Logic 3, no. 1 (2003): 85–118.
    Listed reading
  • Ben-Yaacov, Itay. “Simplicity in Compact Abstract Theories.” Journal of Mathematical Logic 3, no. 2 (2003): 163–191.
    Listed reading
  • Ben-Yaacov, Itay. “Thickness, and a Categoric View of Type-space Functors.” Fundamenta Mathematicae 179 (2003): 199–224.
    Listed reading
  • Ben-Yaacov, Itay. “Lovely Pairs of Models: The Non First Order Case.” Journal of Symbolic Logic 69, no. 3 (2004): 641–662.
    Listed reading
  • Chatzidakis, Zoë, and Anand Pillay. “Generic Structures and Simple Theories.” Annals of Pure and Applied Logic 95 (1998): 71–92.
    Listed reading
  • Kim, Byunghan. “Forking in Simple Unstable Theories.” Journal of the London Mathematical Society 57, no. 2 (1998): 257–267.
    Listed reading
  • Kim, Byunghan. “A Note on Lascar Strong Types in Simple Theories.” Journal of Symbolic Logic 63, no. 3 (1998): 926–936.
    Listed reading
  • Kim, Byunghan, and Anand Pillay. “Simple Theories.” Annals of Pure and Applied Logic 88 (1997): 149–164.
    Listed reading
  • 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.
    Listed reading
  • Wagner, Frank O. Simple Theories. Vol. 503. Mathematics and its Applications. Dordrecht, NL: Kluwer Academic Publishers, 2000. ISBN: 0792362217.
    Listed reading
  • SES #: 1 · TOPICS: The Basic Setting: Universal Domains · READINGS: Ben-Yaacov, Itay. “Positive Model Theory and Compact Abstract Theories.” Journal of Mathematical Logic 3, no. 1 (2003): 85–118.
    Reading assignment
  • Total D-rank and Extension Ben-Yaacov, Itay. “Thickness, and A Categoric View of Type-space Functors.” Fundamenta Mathematicae 179 (2003): 199–224.
    Listed reading
  • SES #: 6 · TOPICS: Lascar Strong Types and the Independence Theorem (Partially taught by Christina Goddard) · READINGS: Ben-Yaacov, Itay. “Simplicity in Compact Abstract Theories.” Journal of Mathematical Logic 3, no. 2 (2003): 163–191.
    Reading assignment
  • SES #: 11-12 · TOPICS: Stable Theories with a Generic Automorphism · READINGS: Chatzidakis, Zoë, and Anand Pillay. “Generic Structures and Simple Theories.” Annals of Pure and Applied Logic 95 (1998): 71–92.
    Reading assignment
  • SES #: 15-16 · TOPICS: Lovely Pairs · READINGS: Ben-Yaacov, Itay. “Lovely Pairs of Models: The Non First Order Case.” Journal of Symbolic Logic 69, no. 3 (2004): 641–662.
    Reading assignment
Sources