Set theory, independence proofs and the continuum hypothesis 1000-2M23STI
Relationship of logic, set theory and mathematics: review of basic notions of logic (proof system, completeness theorem, Lowenheim-Skolem theorem, etc), discussion of mathematics vs metamathematics (2-3 lectures)
Zermelo Fraenkel set theory: axioms, well-ordered sets, ordinals, transfinite induction and recursion (3-4 lectures)
Independence proofs via inner models: independence of the axiom of regularity, constructible universe, absoluteness, consistency of the axiom of choice and continuum hypothesis (4-5 lectures)
Forcing: models of set theory (standard models, minimal model), forcing as a technique, independence of the axiom of choice and the continuum hypothesis (4-5 lectures)
Type of course
Requirements
Course coordinators
Learning outcomes
The student will have understanding of basic notions of set theory, will be able to prove independence results and have a basic working knowledge of the forcing method
Assessment criteria
Oral exam
The course can provide credit for doctoral students as a "methodological course".
In that case, there is an additional requirement for passing the course: The student should correctly solve an assignment given by the lecturer, or study and present a result assigned by the lecturer.
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
- Bachelor's degree, first cycle programme, Computer Science
- Master's degree, second cycle programme, Computer Science
- Master's degree, second cycle programme, Mathematics
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: