- 1.
- Propositional logic: provability, truth tables, consistency, compactness, completeness.
- 2.
- First-order predicate logic: syntax and semantics.
- Deduction systems and formal proofs.
- Consistency, completeness and decidability of theories: the methods of elimination of quantifiers and Vaught's Test.
- Godel's Completeness Theorem. The Henkin proof. The Compactness Theorem and its applications.
- Elementary Model Theory. Elementary substructures and the Lowenheim-Skolem Theorem.
- Godel's Incompleteness Theorem. Applications to undecidable theories.