Abstract
This chapter covers some of the basic theory of Borel and Analytic Sets in the context of the real line. We define analytic sets using the Suslin operation, and show that they have all the regularity properties (measurability, Baire property, perfect set property), and therefore satisfy the continuum hypothesis—the best result possible without additional axioms. Along the way we obtain the Lusin Separation Theorem, Suslin’s theorem, the boundedness theorem, and an example of a non-Borel analytic set.
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