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.
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 style: In presence
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.
Course notes.
FABIO DI BENEDETTO (President)
GIUSEPPE ROSOLINI (President)
RUGGERO PAGNAN
The class will start according to the academic calendar.
MATHEMATICAL LOGIC 1
Standard exam: written essay and oral examination.
Flipped-classroom exam.
Validation of the mathematical knowledge of the basic notions of mathematical logic. Evaluation of the ability to apply that knowlege.
