MATHEMATICAL LOGIC D
Learning outcomes of the course unit
Knowledge of the rudiments of Mathematical Logic, with particular attention to a teaching application of that discipline.
Course contents summary
First-order languages and structures. Satisfaction, truth, validity; logical consequence. Inadequacy of propositional logic. Elementary equivalence. Compactness theorem. An interesting teaching application of the compactness theorem: current infinites and infinitesimals; "calculus" via Non Standard Analysis.
 C. C. CHANG, H. J. KEISLER, Teoria dei modelli , Boringhieri 1980.
 H. ENDERTON, A Mathematical Introduction to Logic, Academic Press 1972.
 H. J. KEISLER, Elementary Calculus. An Infinitesimal Approach, Prindle, Weber & Schmidt 1986.
 K. D. STROYAN, W. A. J. LUXEMBURG, Introduction to the Theory of Infinitesimal, Academic Press 1976.
Another professor collaborates on this course. Exercises are assigned that are then publicly corrected and discussed by the students, under the guidance of one of the professors of the course, during ''laboratory'' hours.