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Published online by Cambridge University Press: 12 March 2014
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 . is there an injective map j : K → ℕ such that j(K) is of degree a and all the functions in ℱ are translated by restrictions of total recursive functions.