different between hyperarithmetic vs hyperjump

English

hyper- +? arithmetic

hyperarithmetic (not comparable)

(mathematics) Pertaining to a generalization of computability theory focusing on certain sets of natural numbers.

hyper- +? jump

hyperjump (plural hyperjumps)

(science fiction) A jump that transports some physical object immediately from one place to another, as by a hyperdrive or jump drive.
(mathematics, logic) A form of Turing jump in hyperarithmetic.

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