Mathematical Logic




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Course Contents

 Formal theories, Consequence and deduction. Propositional Calculus: Syntax, Semantics, Applications; Axiomatic approach, Soundness, Consistency, Completeness. Other proof techniques: Sequent calculus, Tableaux. Boolean Algebras: Properties, Stone's theorem. Completeness of propositional calculus with respect to the class of Boolean algebras. Classical rst order theories: Syntax, Semantics; Axiomatic approach, Soundness; Sequent calculus, Tableaux. Equality, examples of rst order theories with equality. Consistency, Completeness (sketch), Elementary model theory, Decidability. Godel's incompleteness theorems: sketch. 



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