descriptive set theory



Descriptive set theory is the study of the structures and hierarchies of subsets of real numbers (or more generally of subsets of Polish spaces) that are definable by formulas with real parameters in second-order arithmetic.

Such subsets include Borel sets and more generally projective sets that are defined by alternating between taking images under projection maps of previously defined sets and taking complements of previously defined sets. Once the domain of topologists of the Polish schools and Russian analysts of the early 20th century, descriptive set theory is now considered a central area of logic in which set theory and computability theory (recursion theory) meet and interact.