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HU Credits:
2
Degree/Cycle:
2nd degree (Master)
Responsible Department:
Mathematics
Semester:
1st Semester
Teaching Languages:
Hebrew
Campus:
E. Safra
Course/Module Coordinator:
Itay Kaplan
Coordinator Office Hours:
Teaching Staff:
Prof Itay Kaplan
Course/Module description:
A countable structure is called homogeneous if every isomorphism between finite substructures can be extended to an automorphism.
For example, the random graph, dense linear orders, and vector spaces over finite fields.
We will study several topics related to homogeneous structures and their model theory. For example: Fraïssé limits, omega-categoricity, Ramsey structures and the connection with topological dynamics, automorphism groups, and more.
Course/Module aims:
To go over the basics of homogeneous structures and go over some advanced topics.
Learning outcomes - On successful completion of this module, students should be able to:
see aims.
Attendance requirements(%):
Teaching arrangement and method of instruction:
frontal lectures.
Course/Module Content:
Homogeneous structures.
Omega-categoricity. Fraisse limits, examples. Ramsey structures and a bit of Ramsey theory, the connection with topological dynamics. The small index property, the extension property. Connection to classification theory (for example theorems on omega-stable, omega-categorical theories).
Required Reading:
none
Additional Reading Material:
A survey of homogeneous structures by Dugald Macpherson.
Course/Module evaluation:
End of year written/oral examination 0 %
Presentation 0 %
Participation in Tutorials 0 %
Project work 100 %
Assignments 0 %
Reports 0 %
Research project 0 %
Quizzes 0 %
Other 0 %
Additional information:
The grade will be based on a paper submitted by the student.
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