
Detailed information 
Original study plan 
Bachelor's programme Technical Mathematics 2020W 
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 
There will be a written exam at the end of the semester.

Language 
Spanish (and English) 
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 
Further information 
Until term 2020S known as: 201ADMASP2V12 VL Special Topics algebra and discrete mathematics

Earlier variants 
They also cover the requirements of the curriculum (from  to) 201ADMASP2V12: VL Special Topics algebra and discrete mathematics (2012W2020S)

