Inhalt

### [ 201ADMASP1U20 ] UE Special Topics algebra and discrete mathematics

Versionsauswahl
Workload Education level Study areas Responsible person Hours per week Coordinating university
1,5 ECTS B3 - Bachelor's programme 3. year Mathematics Manuel Kauers 1 hpw Johannes Kepler University Linz
Detailed information
Original study plan Bachelor's programme Technical Mathematics 2024W
Objectives In this course (partial) answers to questions like „What is a set“? or „Is there a set which has more elements than the set of natural numbers, but less elements than the set of real numbers?“ are given. After an introduction to model theory we introduce the ZFC (Zermelo-Fraenkel+Choice) axioms of Set Theory. If these axioms are consistent (do not imply a contradiction), then there exists a model of Set Theory, in which all axioms of ZFC are true. Then we develop the method of forcing and prove Cohen’s result, that if there exists a well-founded model of ZFC, then there exists another model of ZFC, in which the Continuum Hypotheses is false.
Subject
1. Ordinal and Cardinal numbers
2. Model Theory
3. The ZFC axioms
4. Boolean-Valued Models of ZFC
5. The Forcing Theorem and the Generic Model Theorem
6. Proof of the consistency and independence of the Continuum Hypotheses
Criteria for evaluation In the exercise sessions homework problems will be discussed.
Language English and French
Study material
1. C.C. Chang, H. Jerome Keisler, Model Theory, third edition, Dover Publications, Inc., Mineola, New York, (2012)
2. T.Jech, Set Theory, The Third Millennium Edition, Springer Monographs in Mathematics, (2002)
Changing subject? Yes
Earlier variants They also cover the requirements of the curriculum (from - to)
201ADMASP1U12: UE Special Topics algebra and discrete mathematics (2012W-2020S)
On-site course
Maximum number of participants 25
Assignment procedure Direct assignment