MATH 7850

MATH 7850

Course information provided by the Courses of Study 2017-2018.

Covers topics in mathematical logic which vary from year to year, such as descriptive set theory or proof theory.  May also be used to further develop material from model theory (MATH 6830), recursion theory (MATH 6840), or set theory (MATH 6870).

When Offered Fall.

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Syllabi: none
  •   Regular Academic Session. 

  • 4 Credits Sat/Unsat

  • 17248 MATH 7850   LEC 001

  • The topic will be Dynamics of Large Groups. The course will focus on continuous actions of non-locally compact groups that are equipped with a complete separable topology (Polish groups). This class of groups includes the unitary group of the separable Hilbert space, homeomorphism groups of compact metric spaces, automorphism groups of countable structures, and the group of measure preserving transformations, among others. The emphasis of the course will be on the structure of orbit equivalence relations and on the structure of continuous actions on compact spaces (flows). In addition to the general introduction to the subject, we will cover the following topics: (1) The Kechris-Louveau theorem identifying a fundamental obstacle for an equivalence relation to be an orbit equivalence relation. (2) Effros-type theorems on embedding of the Vitali equivalence relation into orbit equivalence relations. (3) Universal minimal flows.