SERAFINA LAPENTA | FUNDAMENTALS OF MATHEMATICAL LOGICS
SERAFINA LAPENTA FUNDAMENTALS OF MATHEMATICAL LOGICS
cod. 0522200014
FUNDAMENTALS OF MATHEMATICAL LOGICS
| 0522200014 | |
| DEPARTMENT OF MATHEMATICS | |
| EQF7 | |
| MATHEMATICS | |
| 2024/2025 |
| YEAR OF COURSE 1 | |
| YEAR OF DIDACTIC SYSTEM 2018 | |
| SPRING SEMESTER |
| SSD | CFU | HOURS | ACTIVITY | |
|---|---|---|---|---|
| MAT/01 | 6 | 48 | LESSONS |
| Exam | Date | Session | |
|---|---|---|---|
| ISTITUZIONI DI LOGICA MATEMATICA | 10/01/2025 - 15:00 | SESSIONE DI RECUPERO | |
| ISTITUZIONI DI LOGICA MATEMATICA | 27/01/2025 - 09:00 | SESSIONE DI RECUPERO | |
| ISTITUZIONI DI LOGICA MATEMATICA | 19/02/2025 - 11:00 | SESSIONE DI RECUPERO |
| Objectives | |
|---|---|
| KNOWLEDGE AND UNDERSTANDING: MASTER THE NOTION OF FORMAL THEORY AND THE MAIN TECHNIQUES OF MODEL THEORY AND FORMAL THEORY OF SET AND FORMAL THEORY OF ARITHMETIC. ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING: THE OBJECTIVE OF THE COURSE IS TO MAKE THE STUDENT ABLE TO APPLY THE NOTIONS LEARNED DURING THE LESSONS TO BASIC TROUBLESHOOTING. |
| Prerequisites | |
|---|---|
| IT IS REQUIRED SOME BASIC KNOWLEDGE OF MATHEMATICAL LOGIC TOPICS SUCH AS: PROPOSITIONAL AND FIRST ORDER CALCULUS, BOOLEAN ALGEBRAS. |
| Contents | |
|---|---|
| GODEL'S INCOMPLETENESS THEOREMS (ABOUT 16 HOURS). BASIC ELEMENTS OF UNIVERSAL ALGEBRAS (ABOUT 6 HOURS). VARIETIES AND QUASI-VARIETIES. BIRKHOFF THEOREMS (ABOUT 9 HOURS). ALGEBRIZABLE LOGICS AND THE LINDEMBAUM-TARSKI CONSTRUCTION (ABOUT 9 HOURS). MODAL LOGIC AND LUKASIEWICZ LOGIC (ABOUT 8 HOURS). |
| Teaching Methods | |
|---|---|
| THE 6 CFU COURSE (CORRESPONDING TO 48 HOURS) INCLUDES THEORETICAL LESSONS AIMED AT TEACHING THE BASIC NOTIONS IN THE PROGRAMME AND THE VARIOUS PROOF TECHNIQUES USED. |
| Verification of learning | |
|---|---|
| THE EXAM IS ONLY ORAL AND INCLUDES AN ADDITIONAL SEMINAR. THE SEMINAR WILL FOCUS ON COMPLEMENTARY TOPICS OR ON AN IN-DEPTH ANALYSIS OF A TOPIC COVERED DURING THE COURSE. THE TOPIC WILL BE PREVIOUSLY AGREED WITH THE TEACHER, WHO WILL PROVIDE THE NECESSARY MATERIAL. THE DURATION OF THE SEMINAR IS APPROXIMATELY 30 MINUTES, DURING WHICH THE TEACHER WILL ASK QUESTIONS ON THE TOPICS PRESENTED. TO PASS THE EXAM (MINIMUM GRADE 18/30), THE STUDENT MUST SHOW TO HAVE UNDERSTANDOOD THE FUNDAMENTAL CONCEPTS AND RESULTS OF THE COURSE. STUDENTS WHO DEMONSTRATE COMPLETE AND IN-DEPTH KNOWLEDGE OF ALL THE TOPICS PRESENTED WILL BE ABLE TO RECEIVE A MAXIMUM OF 30/30. HONORS MAY BE AWARDED TO STUDENTS CAPABLE OF AUTONOMOUSLY APPLYING THE KNOWLEDGE AND SKILLS ACQUIRED EVEN IN CONTEXTS OTHER THAN THOSE ADDRESSED DURING THE COURSE AND/OR THE PREPARATION OF THE SEMINAR. |
| Texts | |
|---|---|
| -P. SMITH. GODEL WITHOUT (TOO MANY) TEARS, LOGIC MATTERS, CAMBRIDGE (DISPONIBILE GRATUITAMENTE ONLINE) -C. BERGMAN. UNIVERSAL ALGEBRA: FUNDAMENTAL AND SELECTED TOPICS. CRC PRESS. 2011 -S. BURRIS, H. P. SANKAPPANAVAR. A COURSE ON UNIVERSAL ALGEBRA. (DISPONIBILE GRATUITAMENTE ONLINE) -T. MORASCHINI. THE ALGEBRA OF LOGIC, DISPENSE DEL CORSO DISPONIBILI ONLINE. |
| More Information | |
|---|---|
| FOR FURTHER INFORMATION PLEASE CONTACT THE LECTURERS: SERAFINA LAPENTA (SLAPENTA@UNISA.IT) O LUCA SPADA (LSPADA@UNISA.IT) |
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