Hyperarithmetical Theory
In recursion theory, hyperarithmetic theory is a generalization of Turing computability. It has close connections with definability in second-order arithmetic and with weak systems of set theory such as Kripke–Platek set theory. It is an important tool in effective descriptive set theory.
Read more about Hyperarithmetical Theory: Hyperarithmetical Sets, Example: The Truth Set of Arithmetic, Fundamental Results, Relativized Hyperarithmeticity and Hyperdegrees, Generalizations
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“The struggle for existence holds as much in the intellectual as in the physical world. A theory is a species of thinking, and its right to exist is coextensive with its power of resisting extinction by its rivals.”
—Thomas Henry Huxley (1825–95)