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





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 (ZermeloFraenkel+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 wellfounded model of ZFC, then there exists another model of ZFC, in which the Continuum Hypotheses is false.

Subject 
 Ordinal and Cardinal numbers
 Model Theory
 The ZFC axioms
 BooleanValued Models of ZFC
 The Forcing Theorem and the Generic Model Theorem
 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 
 C.C. Chang, H. Jerome Keisler, Model Theory, third edition, Dover Publications, Inc., Mineola, New York, (2012)
 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 (2012W2020S)




Onsite course 
Maximum number of participants 
25 
Assignment procedure 
Direct assignment 


