Notes on the Theory of Scales

Abstract

It is the purpose of these notes to give an informal exposition of several recent results in Descriptive Set Theory, all centering around the notion of a scale. This was first isolated explicitly in the generalization of the Uniformization Theorem on the hypothesis of projective determinacy [14], but is surely implicit in some of the classical proofs. It has turned out that scales have many applications beyond the Uniformization Theorem, both in producing new results and in providing more elegant proofs of known results.

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