Handouts Part I (Carlucci)
Propositional Logic Primer (up through the Compactness Theorem)
Compactness and Decidability
Konig's Lemma and Compactness
Predicate Logic: Syntax and Semantics
Predicate Logic: General Problems
Back-and-Forth proof of isomorphism
Bounded Equivalence
Duplicator-Spoiler Games
Quantifier Elimination
Undecidability of Arithmetic
Incompleteness of Arithmetic
Decision Problems
Extra reading: Fagin's Theorem, Concrete Independence Results.