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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Degrees of splittings and bases of recursively enumerable subspaces


Authors: R. G. Downey, J. B. Remmel and L. V. Welch
Journal: Trans. Amer. Math. Soc. 302 (1987), 683-714
MSC: Primary 03D45; Secondary 03D25, 03D30
MathSciNet review: 891641
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Abstract: 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 $ {V_\infty }$, we show that $ \alpha $ is the degree of an r.e. basis of $ V$ iff $ \alpha $ is the degree of an r.e. summand of $ V$ iff $ \alpha $ is the degree and dependence degree of an r.e. summand of $ V$. This result naturally leads to explore several questions regarding the degree theoretic properties of pairs of summands and the ways in which bases may arise.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0891641-4
PII: S 0002-9947(1987)0891641-4
Article copyright: © Copyright 1987 American Mathematical Society