Effective descriptive set theory (nonfiction)

Effective descriptive set theory is the branch of descriptive set theory dealing with sets of real numbers having lightface definitions; that is, definitions that do not require an arbitrary real parameter (Moschovakis 1980). Thus effective descriptive set theory combines descriptive set theory with recursion theory.

See also

• Computability theory (nonfiction) - a branch of mathematical logic, of computer science, and of the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has since expanded to include the study of generalized computability and definability. In these areas, recursion theory overlaps with proof theory and effective descriptive set theory. Basic questions addressed by recursion theory include:
  • What does it mean for a function on the natural numbers to be computable?
  • How can noncomputable functions be classified into a hierarchy based on their level of noncomputability?
• Descriptive set theory (nonfiction) - the study of certain classes of "well-behaved" subsets of the real line and other Polish spaces.
• Real number (nonfiction) - a value of a continuous quantity that can represent a distance along a line. The adjective real in this context was introduced in the 17th century by René Descartes, who distinguished between real and imaginary roots of polynomials.
• Set (nonfiction) - a well-defined collection of distinct objects, considered as an object in its own right.

• Effective descriptive set theory @ Wikipedia