CODE 90705 ACADEMIC YEAR 2017/2018 CREDITS 7 cfu anno 1 MATEMATICA 9011 (LM-40) - 7 cfu anno 3 MATEMATICA 8760 (L-35) - SCIENTIFIC DISCIPLINARY SECTOR MAT/01 TEACHING LOCATION SEMESTER 1° Semester TEACHING MATERIALS AULAWEB OVERVIEW The main aim of the course is the study of first order logical theories and their models, to analyse semantic questions, like the completeness and the compactness theorems, as well as syntactic questions, like the incompleteness theorems. AIMS AND CONTENT LEARNING OUTCOMES Study of first-order theories and their models, to analyze semantic issues, such as completeness and compact theorems, and syntactic questions such as incompleteness theorems. TEACHING METHODS Teaching style: In presence SYLLABUS/CONTENT Logic for the mathematical practice and the mathematical teaching. Category theory as the mathematical tool to structure the study of logical theories: categories, functors, natural transformations, adjunctions, indexed categories. Examples from logic: the propositional calculus, first order logic, higher order theories. Formal theories and the deduction calculi. Representation theorems; the completeness theorem for propositional theories and for first order theories. Type theory. The problem of consistency. The mathematical practice and type theory. RECOMMENDED READING/BIBLIOGRAPHY Course notes. TEACHERS AND EXAM BOARD GIUSEPPE ROSOLINI Exam Board FABIO DI BENEDETTO (President) GIUSEPPE ROSOLINI (President) RUGGERO PAGNAN LESSONS LESSONS START The class will start according to the academic calendar. Class schedule MATHEMATICAL LOGIC 1 EXAMS EXAM DESCRIPTION Standard exam: written essay and oral examination. Flipped-classroom exam. ASSESSMENT METHODS Validation of the mathematical knowledge of the basic notions of mathematical logic. Evaluation of the ability to apply that knowlege.
