The development of the descriptive theory of sets under the influence of the work of Luzin

Abstract

CONTENTS Introduction § 0. Euclidean and Baire spaces § 1. Research on the structure of Borel classes § 2. Projective sets. Construction of the hierarchy § 3. The sieve operation and its applications to projective sets of the first level § 4. The first projective level: sets with special sections § 5. The theory of operations on sets. C-sets and R-sets. The second projective level § 6. Difficulties of the classical theory of projective sets. Search for new paths. The main trends of the contemporary development of the descriptive theory § 7. Luzin's problems on the sequence of constituents § 8. Equivalence relations: Luzin's remarks and contemporary research § 9. Problems and results connected with the axiom of choice and transfinite constructions References