Effective descriptive set theory is the branch of descriptive set theory dealing with sets of reals having
lightface definitions; that
Kaynak: Effective descriptive set theoryLightface hierarchy : The
lightface Borel hierarchy is an effective version of the boldface Borel hierarchy. It is important in effective
Kaynak: Borel hierarchy hierarchy of sets classifies sets by the formulas that can be used to define them; it is the
lightface version of the projective hierarchy .
Kaynak: Analytical hierarchyHe is especially associated with the development of the effective , or
lightface , version of descriptive set theory. Moschovakis earned his
Kaynak: Yiannis N. MoschovakisA (
lightface ) Π 0 1 class is a subset C of 2 ω for which there is a computable tree T such that C consists of exactly the paths through T
Kaynak: Π01 classThese devices may be categorized as follows: (1)
lightface and boldface type to indicate when an English word is inserted to complete the
Kaynak: Concordant VersionThe Greek letters here are
lightface symbols, which indicates that the formulas do not contain set parameters. If a formula phi is
Kaynak: Arithmetical hierarchyNote that the bold font in this symbol is not the Wikipedia convention, but rather is used distinctively from its
lightface counterpart
Kaynak: Analytic setIt includes the study of
lightface pointclass es, and is closely related to hyperarithmetical theory . In many cases, results of classical
Kaynak: Set theory