HU Credits:
2
Degree/Cycle:
1st degree (Bachelor)
Responsible Department:
Mathematics
Semester:
1st Semester
Teaching Languages:
Hebrew
Campus:
E. Safra
Course/Module Coordinator:
Yair Hayut
Coordinator Office Hours:
Teaching Staff:
Dr. Hayut Yair
Course/Module description:
During this course we shall introduce the formal framework for Set Theory: The Axiom system of ZermelloFraenkel (ZFC). We shall formally introduce some basic notions like: ordinals, cardinals, wellfoundedness and basic concepts of combinatorial Set Theory. We shall prove some easy cases of independence (For instance the independence of the axiom of replacement)
We shall prove the consistency of the axiom of choice, using the model of hereditarily ordinal definable sets. We shall present the constructible universe (L) and we shall use it to prove the consistency of the Generalized Continuum Hypothesis. Time permitting, we shall talk about an advanced topic at the end of the course (e.g., measurable cardinals, Suslin trees, etc.)
Course/Module aims:
Learning outcomes  On successful completion of this module, students should be able to:
Ability to prove and apply the theorems presented in the course.
Ability to apply correctly the mathematical methodology in the context of the course.
Acquiring the fundamentals as well as basic familiarity with the field which will assist in the understanding of advanced subjects.
Ability to understanding and explain the subjects taught in the course.
Attendance requirements(%):
0
Teaching arrangement and method of instruction:
Course/Module Content:
During this course we shall introduce the formal framework for Set Theory: The Axiom system of ZermelloFraenkel (ZFC). We shall formally introduce some basic notions like: ordinals, cardinals, wellfoundedness and basic concepts of combinatorial Set Theory. We shall prove some easy cases of independence (For instance the independence of the axiom of replacement)
We shall prove the consistency of the axiom of choice, using the model of hereditarily ordinal definable sets. We shall present the constructible universe (L) and we shall use it to prove the consistency of the Generalized Continuum Hypothesis. Time permitting, we shall talk about an advanced topic at the end of the course (e.g., measurable cardinals, Suslin trees, etc.)
Required Reading:
For those who did not take the basic logic course are expected to read about the following topics:
Firstorder language, formulas, sentences, theories, structures, the satisfaction relation, definability, the compactness and completeness theorems (without proof).
Additional Reading Material:
Course/Module evaluation:
End of year written/oral examination 40 %
Presentation 0 %
Participation in Tutorials 0 %
Project work 20 %
Assignments 40 %
Reports 0 %
Research project 0 %
Quizzes 0 %
Other 0 %
Additional information:
The final grade will be composed of midterm assignment (20%), exercises (40%) and a final exam/assignment (40%)
