Handouts Part I (Carlucci)
Handout 1: Syntax and Semantics of First Order Logic. Definability and queries.
Handout 2: Computable function. Representation theorem.
Handout 3: Undecidability of Arithmetic truth. Undefinability of Arithmetic truth. Effective inseparability and Incompleteness.
Handout 4: Machine-independent characterization of computable functions. Sigma-1 formulas. Rice-Shapiro Theorem.
Handout 5: The Arithmetical Hierarchy.
Handout 6: Relative computability. Jump Hierarchy. Post's Theorem.
Handout 7: Analysis of the computational content of Ramsey's Theorem and Hindman's Theorem.
Handout 8: Limit-computable functions. Shoenfields' Limit Lemma. Lower bound for Ramsey for pairs.
Handout 9: The expressibility problem. Compactness. Isomorphism. Elementary equivalence. Bounded elementary equivalence. Back and forth conditions.
Handout 10: Duplicator-Spoiler Games. Logical reductions.
Handouts Part II (Perelli)