First-order logic

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.