Effective descriptive set theory is the branch of descriptive set theory dealing with sets of reals having lightface definitions; that is, definitions that do not require an arbitrary real parameter (Moschovakis 1980).
An effective Polish space is a complete separable metric space that has a computable presentation.
Such spaces are studied in both effective descriptive set theory and in constructive analysis.
Any set that receives a classification is called "arithmetical".
The Greek letters here are lightface symbols, which indicates that the formulas do not contain set parameters.
is logically equivalent to a formula with only bounded quantifiers then
are defined inductively for every natural number n using the following rules:
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