#### General information

**Lectures:** TR 1:00-2:25, Linde 310

**Office:** Linde 308

**Office hours:** M 1:00-3:00, or by appointment

**E-mail:** vidnyanz_at^caltech dot edu

Notes, homeworks

**Grading:** based on weekly homeworks

#### Topics

This term we will cover basics of model theory, first order languages, ultrafilters, Gödel's completeness theorem and the compactness theorem, Löwenheim-Skolem theorems, Fraissé theory and the back-and-forth method, quantifier elimination, and if time permits some applications, such as the solution to Hilbert's 17th problem.28.09: Definition of first order language, formulas, and structures.

30.09: Substructures, elementary equivalence and elementary substructures, Tarski-Vaught.

05.10: Examples of theories, definability.

07.10: Characterization of definability.

12.10: Interpretability.

14.10: Ultrafilters, definition and applications.

19.10: Ultraproducts, Los Lemma.

21.10: The compactness theorem.

26.10: Applications of compactness, nonstandard analysis.

28.10: Godel's completeness theorem.

2.11: Model existence theorem, Henkin construction.

4.11: Extension to Henkin systems.

9.11: Lowenheim-Skolem theorems.

11.11: Lowenheim-Skolem theorems.

16.11: Back-and-forth, DLO's and their properties, the random graph (online).

18.11: Fraisse classes and limits (online).

23.11: Fraisse limits; quantifier elimination (online).

30.11: Quantifier elimination, algebraic criterion.

02.12: Presburger arithmetic.