Prof. Carlucci's Module:
February 26: Presentation of the course. Basics of propositional logic (connectives, formulas, truth-tables, assignments, satisfiability, logical truth, logical consequence, logical equivalence.
February 28: Compactness Theorem for propositional logic (for countable languages).
March 5: Implications of Compactness concerning the decidability of theories.
March 7: Cancelled
March 12: Konig's Lemma is equivalent to the Compactness Theorem. Konig's Lemma is not computably true.
March 14: Syntax and Semantics of Predicate Logic. Satisfaction, truth, validity. Logical consequence. Isomorphism.
March 19: Back and forth proofs of isomorphism for the rational order and for the Random Graph.
March 21: Quantifier rank, bounded elementary equivalence, Back-and-Forth relations, Duplicator-Spoiler Games.
March 26: CANCELLED
March 28: Non expressibility proofs using games. Logical reductions. Games with infinite moves.
April 2: Quantifier Elimination for real addition. Model-theoretic characterization of quantifier elimination.
April 4: The theory of arithmetic. Non-standard models of arithmetic. The class of computable functions. Representation Theorem. Undecidability of arithmetic.
April 9: Inseparability. Incompleteness of arithmetic.
April 11: Effective inseparability. Effective Incompleteness. Mathematical examples of incompleteness. Church's and Traktenbrot's Theorems.
Prof. Perelli's Module:
April 16: Modal Logic: Introduction. Relational Structures.
April 23: Modal Logic: Basic Modal Languages and Modal Languages.
April 30: Frames and Models. Semantics of a Basic Modal Language.
May 2: Cancelled
May 7: Semantics of General Modal Languages. Bidirectional Frames and Models, Regular Frames.
May 9: Frames and Validity. General Frames. Logical Consequence Relation (local and global).
May 14: Normal Modal Logics.
May 16: Invariance results: Disjoint Union, Generated Submodels, Morphisms.
May 21: Bounded Morphisms and tree-like model property.
May 23: Bisimulation and Hennessy-Milner Theorem.
May 28: Cancelled with an invitation to attend the Departmental Distinguished Lecture
May 30: Finite Model Property.