Adequate pointclass
Encyclopedia
In the mathematical field of descriptive set theory
, a pointclass
can be called adequate if it contains all recursive
pointsets and is closed under recursive substitution, bounded
universal and existential quantification and preimages by recursive functions.
Descriptive set theory
In mathematical logic, descriptive set theory is the study of certain classes of "well-behaved" subsets of the real line and other Polish spaces...
, a pointclass
Pointclass
In the mathematical field of descriptive set theory, a pointclass is a collection of sets of points, where a point is ordinarily understood to be an element of some perfect Polish space. In practice, a pointclass is usually characterized by some sort of definability property; for example, the...
can be called adequate if it contains all recursive
Recursive
Recursive may refer to:*Recursion, the technique of functions calling themselves*Recursive function, a total computable function*Recursive language, a language which is decidable...
pointsets and is closed under recursive substitution, bounded
Bounded quantifier
In the study of formal theories in mathematical logic, bounded quantifiers are often added to a language in addition to the standard quantifiers "∀" and "∃". Bounded quantifiers differ from "∀" and "∃" in that bounded quantifiers restrict the range of the quantified variable...
universal and existential quantification and preimages by recursive functions.