Selected topics in decriptive set theory 1000-1M24WTM

mathematics

elective monographs

To attend the course, it is necessary to have the knowledge of set theory somewhat beyond the content of a standard introductory course (including transfinite induction, ordinal and cardinal numbers) and elementary notions of general topology on the level of "Topology I" course.

Student:

1. knows the basics of descriptive set theory, including classical examples of Polish spaces, definitions of Borel and analytic sets as well as sets
with the Baire property and the first category sets,

2. can describe the basic properties of analytic sets,

3. knows the descriptive equivalents of Ramsey's theorem,

4. uses the concept of uniformization and knows the basic theorems about the existence of Borel uniformization.

1. A. S. Kechris, Classical descriptive set theory, Graduate Texts in Math. 156, Springer-Verlag, 1995.

2. S. M. Srivastava, A course on Borel sets, Graduate Texts in Math. 180,Springer-Verlag, 1998.

3. A. W. Miller, Infinite Ramsey theory, lecture notes for Math 873, 1996,
http://www.math.wisc.edu/~miller/old/m873-00/ramsey.pdf.

4. Ch. Rosendal, The dichotomous theories, lecture notes for
Math 511, 2012, http://homepages.math.uic.edu/~rosendal/WebpagesMathCourses/MATH511-2012.html.

5. A. Tserunyan, Introduction to descriptive set theory, lecture notes,
2022, https://www.math.mcgill.ca/atserunyan/Teaching_notes/dst_lectures.pdf.

Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:

• Master's degree, second cycle programme, Mathematics

Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system:

• Description of 1000-1M24WTM in USOSweb