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Abstract. Downey and Remmel have completely characterized the degrees of c.e. bases for c.e. vector spaces (and c.e. fields) in terms of weak truth table degrees. In this paper we obtain a structural result concerning the interaction between the c.e. Turing degrees and the c.e. weak truth table degrees, which by Downey and Remmels classification, establishes the existence of c.e. vector spaces (and...
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