Degrees of splittings and bases of recursively enumerable subspaces

R. G. Downey, J. B. Remmel, L. V. Welch
1987 Transactions of the American Mathematical Society  
This paper analyzes the interrelationships between the (Turing) of r.e. bases and of r.e. splittings of r.e. vector spaces together with the relationship of the degrees of bases and the degrees of the vector spaces they generate. For an r.e. subspace V of Voo , we show that O! is the degree of an r.e. basis of V iff O! is the degree of an r.e. summand of V iff O! is the degree and dependence degree of an r.e. summand of V. This result naturally leads to explore several questions regarding the
more » ... gree theoretic properties of pairs of summands and the ways in which bases may arise. S(V) ~ B(V). It is shown in Remmel [Re!] that a very easy way to manufacture bases is as follows: Let V E L(V 00) and Vl E9 V2 = V be an r.e. splitting of V. Then
doi:10.1090/s0002-9947-1987-0891641-4 fatcat:xhaymjxi3bgglhjz6bwxergbte