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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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by Stephen G. Simpson PDF
Trans. Amer. Math. Soc. 209 (1975), 45-64 Request permission

Abstract:

Every hyperdegree at or above that of Kleene’s $O$ is the hyperjump and the supremum of two minimal hyperdegrees (Theorem 3.1). There is a nonempty $\Sigma _1^1$ class of number-theoretic predicates each of which has minimal hyperdegree (Theorem 4.7). If $V = L$ or a generic extension of $L$, then there are arbitrarily large hyperdegrees which are not minimal over any hyperdegree (Theorems 5.1, 5.2). If ${O^\# }$ exists, then there is a hyperdegree such that every larger hyperdegree is minimal over some hyperdegree (Theorem 5.4). Several other theorems on hyperdegrees and degrees of nonconstructibility are presented.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 209 (1975), 45-64
  • MSC: Primary 02F30
  • DOI: https://doi.org/10.1090/S0002-9947-1975-0392534-3
  • MathSciNet review: 0392534