# New Directions in Descriptive Set Theory

@article{Kechris1999NewDI, title={New Directions in Descriptive Set Theory}, author={Alexander S. Kechris}, journal={Bulletin of Symbolic Logic}, year={1999}, volume={5}, pages={161 - 174} }

§1. I will start with a quick definition of descriptive set theory: It is the study of the structure of definable sets and functions in separable completely metrizable spaces. Such spaces are usually called Polish spaces. Typical examples are ℝ n , ℂ n , (separable) Hilbert space and more generally all separable Banach spaces, the Cantor space 2ℕ, the Baire space ℕℕ, the infinite symmetric group S∞, the unitary group (of the Hilbert space), the group of measure preserving transformations of the…

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