Mathematical Logic 1

A.Y. 2020/2021
9
Max ECTS
63
Overall hours
SSD
MAT/01
Language
Italian
Learning objectives
Knowledge of a calculus for first order logic; proofs formalization
abilities in formal number theory and in other mathematical theories.
Expected learning outcomes
Knowledge of the main semantic completeness proofs; knowledge of
classical negative results by Godel and Church.
Course syllabus and organization

Single session

Responsible
Lesson period
First semester
The course program is not subject to changes; however lectures will be delivered from remote, preferably in synchronous mode. Detailed practical information will be available from the Ariel platform before the beginning of the lectures.
Prerequisites for admission
The course does not have special prerequisites.
Assessment methods and Criteria
Oral examination.
Logica matematica 1 (prima parte)
Course syllabus
Tarski semantocs for first order logic.
Theories and examples of theories.
Sequent calculus.
Completeness theorem.
Elements of recursion theory.
Godel theorems (with some essential analysis form an historical and an epistemological perspective).
Teaching methods
Lectures from remote using Microsoft Teams platform.
Teaching Resources
Electronic notes available from Arial platform.
Logica matematica 1 (mod/02)
Course syllabus
Ultrafilters, ultraproducts.
Los Theorem.
Non standard models of the reals.
Applications to analysis and to Ramsey theory (to be chosen according to students' interests).
Teaching methods
Lectures from remote in synchronous mode.
Teaching Resources
Electronic notes available from Arial platform from December.
Logica matematica 1 (mod/02)
MAT/01 - MATHEMATICAL LOGIC - University credits: 3
Lessons: 21 hours
Logica matematica 1 (prima parte)
MAT/01 - MATHEMATICAL LOGIC - University credits: 6
Lessons: 42 hours
Professor: Ghilardi Silvio