Generalized weak presentations

Journal of Symbolic Logic 67 (2):787-819 (2002)
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Let K be a computable field. Let F be a collection of recursive functions over K, possibly including field operations. We investigate the following question. Given an r.e. degree a, is there an injective map j: K $\longrightarrow \mathbb{N}$ such that j(K) is of degree a and all the functions in F are translated by restrictions of total recursive functions



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Possible degrees in recursive copies II.C. J. Ash & J. F. Knight - 1997 - Annals of Pure and Applied Logic 87 (2):151-165.
Uncountable degree spectra.Valentina S. Harizanov - 1991 - Annals of Pure and Applied Logic 54 (3):255-263.
Possible degrees in recursive copies.C. J. Ash & J. F. Knight - 1995 - Annals of Pure and Applied Logic 75 (3):215-221.

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