Prof. Carlucci's Module:
March 2: Presentation of the course. The language of First-Order Logic. Syntax and Semantics. (3h)
March 5: Formulas and Sentences. General Logical Problems. The class of Computable Functions. (2h)
March 9: Definability of computable functions in arithmetic. Undecidability of the Halting Problem. Undecidability of Arithmetic. (3h)
March 12: Undecidability of Arithmetic. Inseparable pairs. Effectively inseparable pairs. Effective version of Arithmetic Incompleteness. (2h)
March 19: Machine-independent characterization of computable functions and c.e. sets. Sigma1 and Pi1 formulas. Rice-Shapiro Theorem. (2h)
March 24: The Arithmetical Hierarchy. Ramsey's Theorem. Computable instances with no computable solution. (2h)
March 26: Oracle computability. Turing jump. Jump Hiearchy. Post's Theorem. Complexity of Hindman's Finite Sums Theorem. (2h)
March 30: Mind-changing algorithms. Limit-computable functions. Shoenfield's Limit Lemma. Lower bound on Ramsey for pairs. (3h)
April 9: Expressibility of properties over a class of structures. Compactness arguments and their limitations. Isomorphism and elementary equivalence. (2h)
April 10: Bounded elementary equivalence. Back and forth conditions. Method for non-expressibility proofs. (2h)
April 14: Duplicator-Spoiler games. Logical reductions. (2h)
April 17: Seminar by Navid Talebanfard. "Depth-Three Circuits: Recent Constructions and Lower Bounds, and the Road Ahead". (2h)
April 21: Seminar by Noam Greenberg. "Reverse mathematics of Cousin’s lemma". (2h)
Prof. Perelli's Module:
April 23: Relational Structures. (2h)
April 27: Basic Modal Language. Modal Languages. (3h)
April 30: Frames and Models. Semantics of a Basic Modal Language. (2h)
May 4: Semantics of General Modal Languages. Bidirectional Frames and Models, Regular Frames. (3h)
May 7: Frames and Validity. General Frames. Logical Consequence Relation (local and global). Normal Modal Logics. (2h)
May 11: Invariance results: Disjoint Union, Generated Submodels, Morphisms. (3h)
May 14: Bounded Morphisms and tree-like model property. (2h)
May 18: Bisimulation and Hennessy-Milner Theorem. (3h)
May 21: Finite Model Property by submodel selection. (2h)
May 25: Finite Model Property by Filtration. Standard Translation. (3h)