|ELEMENTI DI TEORIA DEGLI INSIEMI||MAT/01||LEZIONI||60|
The student who successfully completes the course will be aquainted with the Zermelo-Fraenkel axiomatic system ZFC for set theory with the axiom of choice and with how ZFC may serve as a formalization of mathematics. He/she will be able to demonstrate a solid knowledge of cardinal and ordinal numbers and their use.
The student will be assessed on his/her demonstrated ability to discuss the main course contents using the appropriate terminology. During the oral exam the student must be able to demonstrate his/her knowledge of the course material and to demonstrate propriety of expression. In the written exam (2 hours, 4 problems), the student must demonstrate his/her knowledge of the course material and to solve the proposed problems.
- Final written exam
- Final oral exam
Delivery: face to face
- attending lectures
- individual study
- Bibliography search
Zermelo-Fraenkel axiomatic set theory with axiom of choice. Formalization of mathematics. Equivalent formulations of the axiom of choice. Cardinal numbers. Well-orderings and ordinal numbers. Cardinal and ordinal algebras. Natural models.
Hrbacek-Jech, Introduction to Set Theory. Recommended readings: Stoll, Set Theory and Logic; Kunen, Set Theory; Jech, Set Theory; Levy, Basic Set Theory
Final written exam. Final oral exam.