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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Degrees of splittings and bases of recursively enumerable subspaces
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by R. G. Downey, J. B. Remmel and L. V. Welch PDF
Trans. Amer. Math. Soc. 302 (1987), 683-714 Request permission

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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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 302 (1987), 683-714
  • MSC: Primary 03D45; Secondary 03D25, 03D30
  • DOI: https://doi.org/10.1090/S0002-9947-1987-0891641-4
  • MathSciNet review: 891641