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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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The number of certain integral polynomials and nonrecursive sets of integers, Part 2
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by Harvey M. Friedman PDF
Trans. Amer. Math. Soc. 357 (2005), 1013-1023 Request permission

Abstract:

We present some examples of mathematically natural nonrecursive sets of integers and relations on integers by combining results from Part 1, from recursion theory, and from the negative solution to Hilbert’s 10th Problem.
References
  • Piergiorgio Odifreddi, Classical recursion theory, Studies in Logic and the Foundations of Mathematics, vol. 125, North-Holland Publishing Co., Amsterdam, 1989. The theory of functions and sets of natural numbers; With a foreword by G. E. Sacks. MR 982269
  • Handbook of mathematical logic, Studies in Logic and the Foundations of Mathematics, vol. 90, North-Holland Publishing Co., Amsterdam, 1977. With the cooperation of H. J. Keisler, K. Kunen, Y. N. Moschovakis and A. S. Troelstra. MR 457132
  • T. Erdélyi, H. Friedman, The number of certain integral polynomials and nonrecursive sets of integers, Part 1, this issue.
  • Hilary Putnam, An unsolvable problem in number theory, J. Symbolic Logic 25 (1960), 220–232. MR 158825, DOI 10.2307/2964679
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Additional Information
  • Harvey M. Friedman
  • Affiliation: Department of Mathematics, Ohio State University, Columbus, Ohio 43210
  • MR Author ID: 69465
  • Email: friedman@math.ohio-state.edu
  • Received by editor(s): July 15, 2003
  • Published electronically: October 5, 2004
  • © Copyright 2004 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 357 (2005), 1013-1023
  • MSC (2000): Primary 03D20, 03D80; Secondary 11U05
  • DOI: https://doi.org/10.1090/S0002-9947-04-03632-3
  • MathSciNet review: 2110430