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Hyperarithmetical theory

In computability 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.

Hyperarithmetical sets and iterated Turing jumps: the hyperarithmetical hierarchy, Fundamental results & Hyperarithmetical sets and constructibility