Title

Details

Lecture

Exercise

Formal Languages and Systems

Motivations, brief historic account, formal languages, structural induction, formal systems.

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Propositional Calculus 
Syntax, models and satisfiability, semantic deduction, normal forms.

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Proofs in Propositional Calculus

Syntactic deduction, deduction theorem, consistency, proof by contradiction theorem, soundness.

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Completeness of Propositional Calculus

Maximal consistency, completeness theorem.

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Compactness of Propositional Calculus

The compactness theorem, definability, coloring infinite graphs.

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Predicate Calculus

Syntax, models and satisfiability, normal forms.

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Proofs in Predicate Calculus

Axioms, syntactic deduction, generalization theorem, soundness.

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Completeness of Predicate Calculus

Closed and complete consistent sets, completeness theorem.

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Compactness of Predicate Calculus

LöwenheimSkolem special case, definability, second order logic.

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