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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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$\beta$-recursion theory
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by Sy D. Friedman PDF
Trans. Amer. Math. Soc. 255 (1979), 173-200 Request permission

Abstract:

We define recursion theory on arbitrary limit ordinals using the J-hierarchy for L. This generalizes $\alpha$-recursion theory, where the ordinal is assumed to be ${\Sigma _1}$-admissible. The notion of tameness for a recursively enumerable set is defined and the degrees of tame r.e. sets are studied. Post’s Problem is solved when ${\Sigma _1}\operatorname {cf} \beta \beta {\ast }$. Lastly, simple sets are constructed for all $\beta$ with the aid of a $\beta$-recursive version of Fodor’s Theorem.
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Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 255 (1979), 173-200
  • MSC: Primary 03D60; Secondary 03E45
  • DOI: https://doi.org/10.1090/S0002-9947-1979-0542876-7
  • MathSciNet review: 542876