|Wednesday||11:30 AM - 1:30 PM||lesson||Lecture Hall M|
|Friday||11:30 AM - 1:30 PM||lesson||Lecture Hall M|
The teaching of mathematics faces relevant problems due to the difficult relationship between syntax and semantics. The goal of this course will be to study the relationship between syntax and semantic, showing the potentialities and the limits of formal languages.
First order languages, validity and completeness results for these languages. Compactness theorem and the strengthening of the completeness theorem. The problem of the decidability of the syntactic control of the satisfiability of a set of formulas.The Lowenheim - Skolem theorems and non categorical theories. Skolem's paradox. Categoricity of the theory of a specific finite structure. Confutation trees for denumerable languages. Sequents, natural deduction and the syntactic analysis of validity. Hilbert's style deduction and the related theorems of validity and completeness. Propositional calculus. Higher order logics. Sketch of the Goedel's incompleteness theorems.
Either open questions written exam or oral exam depending on the number of candidates attending the session.
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