The emergence of descriptive set theory
pp. 241-262
in: Jaakko Hintikka (ed), From Dedekind to Gödel, Berlin, Springer, 1995Abstract
Descriptive set theory is the definability theory of the continuum, the study of the structural properties of definable sets of reals. Motivated initially by constructivist concerns, a major incentive for the subject was to investigate the extent of the regularity properties, those properties indicative of well-behaved sets of reals. With origins in the work of the French analysts Borel, Baire, and Lebesgue at the turn of the century, the subject developed progressively from Suslin's work on the analytic sets in 1916, until Gödel around 1937 established a delimitative result by showing that if V = L, there are simply defined sets of reals that do not possess the regularity properties. In the ensuing years Kleene developed what turned out to be an effective version of the theory as a generalization of his foundational work in recursion theory, and considerably refined the earlier results.