Mikhail Yakovlevich Souslin.
Mikhail Yakovlevich Souslin.
Descriptive set theory, Fall 2007
Instructor: Christian Rosendal, room 304 Altgeld Hall
Course hours: 10:00 - 10:50 AM, MWF.
Location: Room 441, Altgeld Hall.
Homework sets:
This is a course covering the core material of classical descriptive set
theory. Descriptive set theory concerns the structure and regularitry
properties of definable subsets of Polish spaces, e.g., definable subsets
of the reals. It is well-known that using the axiom of choice bad sets
of reals can be constructed, e.g., non-measurable sets, but if one only
consider sets that are defined explicitly provably such sets do not occur.
Descriptive set theory is the study of these explicitly defined sets.
Descriptive set theory thrives in its interactions with other branches
of mathematics such as the study of inner models of set theory, the
geometry of Banach spaces, ergodic theory, and harmonic analysis and
has proved to be a useful tool in all of these domains. So the course
will be of interest to the general abstract analyst. Among the topics
we will cover are:
Much of the material will presuppose a certain maturity in analysis
that can be gained from courses on measure theory, functional analysis,
or general topology. A knowledge of set theory is also useful but not
essential. There are no specific required prerequisites.
Required reading:
Other suggested reading:
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