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Last updated:

November 7, 2022

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

Description

This is an advanced topics course in model theory whose main theme is simple theories.

We treat simple theories in the framework of compact abstract theories, which is more general than that of first order theories. We cover the basic properties of independence (i.e., non-dividing) in simple theories, the characterization of simple theories by the existence of a notion of independence, and hyperimaginary canonical bases

Course Curriculum

  • The Basic Setting: Universal Domains Unlimited
  • Extraction of Indiscernible Sequences Unlimited
  • Dividing and its Basic Properties Unlimited
  • Simplicity Unlimited
  • Thickness Unlimited
  • Lascar Strong Types and the Independence Theorem Unlimited
  • Examples: Hilbert Spaces, Hyperimaginary Sorts Unlimited
  • Generically Transitive Relations Unlimited
  • Characterisation of Simplicity and Non-dividing in Terms of Abstract Notion of Independence Unlimited
  • Supersimplicity Unlimited
  • Stable Theories with a Generic Automorphism Unlimited
  • Groups: Stratified Ranks, Generic Elements and Types Connected Components, Stabilisers Unlimited
  • Lovely Pairs Unlimited

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Massachusetts Institute of Technology