NMAK17004U CANCELLED: Introduction to Descriptive Set Theory (DesSet)

Knowledge: The student should know the definitions of Polish spaces, standard Borel spaces, and examples of these, as well as the definition of the Borel hierarchy, of analytic sets, and for their tree analysis; Lusin's separation theorem and its consequences, and the regularity properties of analytic sets; the selection problem for Borel relations, as well as the Jankov-von Neumann selection theorem, and the selection principle for Borel relations with countable sections; the concenpt of genericity together with the Kuratowski-Ulam theorem; the concept of Borel reducibility, and the basic dichotomies of Silver and Harrington-Kechris-Louveau.

Skills: The student should be able to apply descriptive set theoretic concepts and result mentioned in the previous paragraph to prove borelness/analyticity of a relation/function, check whether a given set is generic/meager, apply basic dichotomies to equivalence relations and solve other problems related to the material of the course.

Competences:  The student should be able to formulate the main results of the course, check whether they are applicable in a concrete problem and use them to solve it.