Mathematical Logic 1
A.Y. 2021/2022
Learning objectives
Knowledge of a calculus for first order logic; ability to
formalize proofs (in particular, to work in a theory formal numbers).
For the 3 credits complement: introduction to the methods of nonstandard analysis.
formalize proofs (in particular, to work in a theory formal numbers).
For the 3 credits complement: introduction to the methods of nonstandard analysis.
Expected learning outcomes
Knowledge of the main semantic completeness techniques;
knowledge of the limiting results of Godel and Church.
For the complement of 3 credits: knowledge of the definition of ultrafilter and ultraproduct, of Los Theorem, of models of nonstandard analysis and their properties.
knowledge of the limiting results of Godel and Church.
For the complement of 3 credits: knowledge of the definition of ultrafilter and ultraproduct, of Los Theorem, of models of nonstandard analysis and their properties.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Prerequisites for admission
The course does not have special prerequisites.
Assessment methods and Criteria
Oral examination.
Logica matematica 1 (prima parte)
Course syllabus
Tarski semantics 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).
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
Standard lectures and guided exercises
Teaching Resources
Electronic notes available from Arial platform.
Logica matematica 1 (mod/02)
Course syllabus
Ultrafilters, ultraproducts, Los theorem.
Models of nonstandard analysis and their properties.
Models of nonstandard analysis and their properties.
Teaching methods
Standard teacher lectures
Teaching Resources
Electronic notes available from Ariel platform.
Logica matematica 1 (mod/02)
MAT/01 - MATHEMATICAL LOGIC - University credits: 3
Lessons: 21 hours
Professor:
Ghilardi Silvio
Logica matematica 1 (prima parte)
MAT/01 - MATHEMATICAL LOGIC - University credits: 6
Lessons: 42 hours
Professor:
Luperi Baglini Lorenzo
Professor(s)