Syllabus
We will study basic methods for proving algorithmic decidability of first-order theories and main examples of decidable theories.
Tools:
- quantifier elimination
- interpretations
- Ehrenfeucht-Fraïssé games
- Mostowski and Feferman-Vaught theorems
- Fraïssé limits
Exhibits (depending on time constraints):
- theories of abelian groups and modules
- ordered abelian groups (divisible, Presburger arithmetic)
- algebraically closed and real-closed fields
- theories of linear orders
- theories of Boolean algebras
- theories of random structures
- theories of locally free algebras
- Skolem arithmetic
Annotation
Non-repeated universal elective course.
In 2023/24: Decidable theories.
We will study basic methods for proving algorithmic decidability of first-order theories and main examples of decidable theories.