Model Theory

PhD Course in Computer Science, Mathematics and Physics

2020-2021

Model Theory

Advanced Course

Lecturer

Silvia Barbina
The Open University (UK)
Board Contact
Alberto Marcone
SSD
MAT/01
CFU
4 CFU + assignment: 2 CFU
Period
January–February 2021
Lessons / Hours
8 lessons, 16 hours, online
Program

We introduce some model-theoretic tools and ideas up to initial notions in stability theory. We aim to cover a selection of the following topics:

  • types, the compactness theorem for types
  • examples of relational structures (dense linear orders, the random graph)
  • universal homogeneous models
  • saturation and the existence of saturated models
  • the monster model
  • omitting types theorem, small theories
  • ω-categorical theories and the Ryll-Nardzewski theorem
  • preservation theorems and quantifier elimination
  • imaginaries and the eq-expansion
  • formulas without the order property (externally definable sets, stability and the number of types)
Prerequisites

Structures, theories, elementarity (including elementary substructures, Tarski-Vaught test, downward Lowenheim-Skolem theorem), the compactness theorem.