HU Credits:
3
Degree/Cycle:
1st degree (Bachelor)
Responsible Department:
Mathematics
Semester:
2nd Semester
Teaching Languages:
Hebrew
Campus:
E. Safra
Course/Module Coordinator:
Yair Hayut
Coordinator Office Hours:
By appointment
Teaching Staff:
Dr. Hayut Yair
Course/Module description:
In the beginning of the 20th century mathematicians tried to find a complete system of axioms for the whole of mathematics and in particular for number theory.
Godel showed that these efforts cannot succeed: Godel's incompleteness theorem says that in any reasonable system of axioms there is always a true statement which cannot be proved.
In the course we will review the incompleteness theorems and relevant parts of recursion theory. We will also learn about Peano Arithmetic.
In addition the course includes an introduction to model theory.
Course/Module aims:
See learning outcomes.
Learning outcomes - On successful completion of this module, students should be able to:
1) Formulate and prove Godel's first and second incompleteness theorems.
2) Explain about the difference between provability and truth to the nearest crank.
3) Prove some basic facts about models of PA.
4) Translate claims about computers (or Turing machines) to arithmetic.
Attendance requirements(%):
0
Teaching arrangement and method of instruction:
Lecture+exercise
Course/Module Content:
This is a list of some of the subjects that will be covered in the course:
Godel's incompleteness theorems on Peano arithmetic.
Tarski's undefinability of truth theorem.
Recursion theory: recursive function, the recursion theorem, RE sets.
Model theory: ultraproducts, compactness, Lowenheim-Skolem theorems.
Models of Peano Arithmetic.
We may learn more/other subjects.
Required Reading:
none
Additional Reading Material:
R. Smullyan, Godel's Incompleteness Theorems
R. Kaye, Models of Peano Arithmetic
J.L. Bell and M. Machover, A Course in Mathematical Logic
J.R. Shoenfield, Mathematical Logic
H. Enderton, A Mathematical Introduction to Logic
Grading Scheme :
Essay / Project / Final Assignment / Home Exam / Referat 50 %
Submission assignments during the semester: Exercises / Essays / Audits / Reports / Forum / Simulation / others 50 %
Additional information:
50% of the grade will be based on students presenting solutions to exercises during the semester and a final assignment.
Lecture recordings will be available after each class.
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