"Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees."
Study of computability and undecidability.
"[...], the study of computable functions and Turing degrees."
"[...], originated in the 1930s."
"The field has since expanded to include the study of generalized computability and definability."
"In these areas, computability theory overlaps with proof theory and effective descriptive set theory."
"Basic questions addressed by computability 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?"
"mathematical computability theorists study the theory of relative computability, reducibility notions, and degree structures"
"those in the computer science field focus on the theory of subrecursive hierarchies, formal methods, and formal languages."
"Computability theory, also known as recursion theory"
"computability theory overlaps with proof theory"
"computability theory overlaps with effective descriptive set theory."
"The study of generalized computability and definability"
"[...], the theory of relative computability"
"[...], reducibility notions"
"[...], and degree structures"
"[...], the theory of subrecursive hierarchies"
"[...], formal methods"
"[...], and formal languages."