Characteristic Properties of Majorant-Computability over the Reals
نویسندگان
چکیده
Characteristic properties of majorant-computable real-valued functions are studied. A formal theory of computability over the reals which satisses the requirements of numerical analysis used in Computer Science is constructed on the base of the deenition of majorant-computa-bility proposed in 13]. A model-theoretical characterization of majorant-computability real-valued functions and their domains is investigated. A theorem which connects the graph of a majorant-computable function with validity of a nite formula on the set of hereditarily nite sets on IR, HF(IR) (where IR is a proper elementary enlargement of the standard reals) is proven. A comparative analysis of the deenition of majorant-computability and the notions of computability earlier proposed by Blum et al., Edalat, S underhauf, Pour-El and Richards, Stoltenberg-Hansen and Tucker is given. Examples of majorant-computable real-valued functions are presented.
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