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Descriptive set theory, Fall 2007
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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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