Mathematical Logic 1
A.Y. 2025/2026
Learning objectives
The course aims to introduce the essential topics of Mathematical Logic, thus allowing the students to learn the relationships between the syntactic part of Logic, concerning deductive calculus, and the semantic part, concerning mathematical models.
Expected learning outcomes
At the end of the course students should be able to know the relationships between logical consequence and semantical truth, know how to do deductive calculations, know and apply the theorems of completeness and compactness, recognize recursive functions, know the relationship between recursion and logical representability, know the main theories of arithmetic and understand Gödel's limititative results.
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
Course syllabus
Tarski semantics for first order logic.
Theories and examples of theories.
Sequent calculus.
Completeness theorem.
Recursive functions and representability.
Goedel Theorems.
Theories and examples of theories.
Sequent calculus.
Completeness theorem.
Recursive functions and representability.
Goedel Theorems.
Prerequisites for admission
The course does not have special prerequisites.
Teaching methods
Standard teacher lectures
Teaching Resources
Electronic notes available from Ariel platform.
Assessment methods and Criteria
Oral examination; students willing to do both modules can split the oral examination in two parts, one for each module. The final grade is unique.
MAT/01 - MATHEMATICAL LOGIC - University credits: 9
Practicals: 24 hours
Lessons: 49 hours
Lessons: 49 hours
Professors:
Luperi Baglini Lorenzo, Reggio Luca
Professor(s)